




































































A 


TREATISE 


ON 

SURVEYS G, 

• * t 

CONTAINING 

THE THEORY AND PRACTICE: 


i 


TO WHICH IS PREFIXED, 

A PERSPICUOUS SYSTEM 

OF 

PLANE TRIGONOMETRY. 


THE WHOLE 


CLEARLY DEMONSTRATED AND ILLUSTRATED 

p ( ' ' ' 


T’ 


BY 


A LARGE NUMBER OF APPROPRIATE EXAMPLES. 

) 1 *, 

PARTICULARLY ADAPTED TO THE USE OF SCHOOLS. 


BY JOHN GUMMERE, A. M. 

1 i 

FELLOW OF THE AMERICAN PHILOSOPHICAL SOCIETY, AND CORRESPONDING 
MEMBER OF THE ACADEMY OF NATURAL SCIENCES, PHILADELPHIA. 


FIFTH EDITION, IMPROVED. 


. ' ' 

V. 


W'%. 

PHILADELPHIA : 

KIMBER AND SHARPLESS, NO. 8, SOUTH FOURTH STREET. 

ADAM WALDIE AND CO. PRINTERS. 



1828. 

L- 








V 


- • > r % \ \ v 






-mt — , / _ § 

Eastern District of Pennsylvania , to mf ; 

BE IT REMEMBERED, that, on the second day of September, in the fif¬ 
tieth year of the Independence of the United States of America, A. D. 1825, John 
Richardson and Kimber Si Sharplcss of the said district have deposited in this 
office the title of a book, the right whereof they claim as proprietors, in the 
words following :—To wit : 

“ A Treatise on Surveying, containing the Theory and Practice : to which is 
“ prefixed, a perspicuous System of Plane Trigonometry. The whole clearly 
“ demonstrated, and illustrated by a large number of appropriate Examples. 
“ Particularly adapted to the use of Schools. By John Gummere. Fourth 
“ edition, improved.” 

In conformity to the act of the Congress of the United States, entitled “ An 
Act for the Encouragement of Learning, by securing the copies of Maps, Charts, 
and Books, to the authors and proprietors of such copies, during the times 
therein mentioned.” And also to the act, entitled “ An act supplementary to 
an Act, entitled, ‘ An Act for the Encouragement of Learning, by securing the 
copies of Maps, Charts, and Books, to the authors and proprietors of such copies 
during the times therein mentioned,’ and extending the benefits thereof to the 
arts of designing, engraving, and etching historical and other prints.” 

D. CALDWELL, 

Clerk of the Eastern District of Pennsylvania. 


/ A ^ fs 





RECOMMENDATIONS. 


I am much pleased with the Treatise on Surveying, compiled by John Gum- 
mere, and hope to see it speedily introduced into general use. With those who 
appreciate its merits, I apprehend it will supersede every other tract on the sub¬ 
ject with which I am acquainted. 

ENOCH LEWIS. 


We have no hesitation in giving it as our judgment, that Gummere’s Treatise 
on Surveying is the best publication on the subject with which we are acquaint¬ 
ed, and we, accordingly, take great pleasure in recommending it to the public 
patronage. 

R. PATTERSON, 

Vice president of the American Philosophical Society. 

R. M. PATTERSON, M. D. 

Prof, of Math, and Mat. Phil, in the Univer. of Pennsylvania. 
— 

The new Treatise on Surveying by John Gummere, recently published by 
Kimber and Richardson, of Philadelphia, is, in our estimation, a very judicious 
performance. 

Several things are omitted which only serve to encumber other works on this 
subject, and a variety of new rules and illustrations are introduced, particularly 
under the heads of laying out, measuring, and dividing land, which, in connec¬ 
tion with its general arrangement, render this Treatise on Surveying, in our 
opinion, decidedly preferable to any other which has met the public eye. 

ROBERT ADRAIN, 

Prof, of Math, and Mat. Phil. Columbia College, Mew York. 

JOHN GRISCOM, 

Teacher of Math. Prof of Chem. Colum. Col. Mew York. 


Having carefully examined a Treatise on Surveying, by John Gummere, I feel 
myself perfectly justifiable in pronouncing it to be the best practical work on 
t he subject extant, 

DAVID M‘CLURE, 

Principal of the Maul, and Math. Arad. Philadelphia. 






IV 


RECOMMENDATIONS. 


\ 


The following letter was addressed by the late Professor of Mathematics, Sic. in Ver- 
mont College, to R. M. Patterson, M. D. Prof, of Math, and Mat. Phil, in the 
University of Pennsylvania. 


Philadelphia, July 16, 1814. 

Dear sir, 

Agreeably to your request I have cursorily examined Gummere’s Treatise on 
Surveying, and conceive that the author has performed all that his preface promi¬ 
ses. The subject is logically distributed and arranged, and the principles correct- 
ly and perspicuously displayed. The examples are very properly multiplied and 
ingeniously varied, so as to prepare the student for the most unusual cases. 
That the author’s success in the publication may equal his high reputation for 
science, is a wish, which (as far as good wishes go) ought to be as satisfactory 
to him, as it is sincere on the part of 

Yours with very high respect and esteem, 


JAMES DEAN. 


/ 


Extract from a letter from Samuel Knox, Esq. principal of the Baltimore College. 
“ I received and submitted to our Mathematical Professor, Gummere’s Sur¬ 
veying. We approve of the work, and as often as any of our students want an 
author on that branch, we shall recommend it.” 

I remain very respectfully, your 

obedient, humble servant, Sic. 

SAMUEL KNOX. 


I fully concur with the gentlemen who have already given recommendations 
of Gummere’s Treatise on Surveying, in considering the work as well calcu¬ 
lated to give youth a correct knowledge of the principles of Surveying, and that 
it is to be preferred to any treatise on that subject, known in this country. 

ELIJAH SLACK, 
Prof, of Math, in Princeton College. 


For sale by the publishers : Solutions to the Miscellaneous Questions in 
Gummere’s Surveying. By the Author. Price twenty-five cents. 

Also a Stereotype edition of Mathematical Tables, containing Tables of Lati¬ 
tude and Departures, of Logarithms from one to ten thousand ; and artificial 
Sines, Tangents and Secants; the whole carefully revised and compared with 
the most correct European editions. 





I 


-a. ' ’> y » t ,' 

\ \ 

mJ', U ' ' \ ' ■ ' 

' 1 " v ,v . , y . 

PREFACE. 

• * 


THE following compilation originated in the belief that our 
schools are in want of a treatise on surveying, adapted to the 
methods practised in this country, and freed from the defects of 
the systems now in use. Notwithstanding the importance of the 
science, and the large number that make it an object of study, it 
is believed we are not in possession of a treatise on this subject, 
suited to the wants of the student. The works of Gibson and 
Jess are the only ones at present in general use; the former, 
though much the better of the two, is deficient in many respects. 
It may be sufficient here, merely to advert to its want of exam¬ 
ples, which renders it entirely unsuitable for a school book. 
From the latter, the student would in vain expect to become ac¬ 
quainted with the principles of the science, or the rationale of 
any of the rules, necessary in performing the various calcula¬ 
tions.* 

1 

In order to understand the principles of surveying, a previous 
knowledge of Geometry is absolutely necessary ; and this know¬ 
ledge will be best acquired from a regular treatise on the subject. 
In the demonstrations, therefore, throughout this work, the student 
is supposed to be acquainted with the elements of that science. 
The references are adapted to Playfair’s Geometry, but they will 

* Each of these works has lately gone through a new edition, in which consi¬ 
derable additions are stated to have been made. On examination, however, it 
does not appear, that those additions are such as to supply the deficiencies. 

The additions made to Gibson, consists principally of some nautical problems 
quite foreign to a treatise on Surveying. Those made to Jess, consist of a few 
extracts from Gibson, in one of which the Pennsylvania method of calcula¬ 
tion is introduced, as being quite different from that given by Jess ; whereas it 
is well known to be the method given by that author, and used, as well in the 
preceding, as in the subsequent part of his work. 

.■ 1 ’ i- : 



W' 



VI PREFACE. 

in general apply equally well to Simson’s translation of Euclid’s 
Elements. 

As there are many who wish to obtain a practical knowledge 
of Surveying, whose leisure may be too limited to admit of their 
going through a course of Geometry, the author has adapted his 
work to this class, by introducing the necessary geometrical defi¬ 
nitions and problems, and by giving plain and concise rules, en¬ 
tirely detached from the demonstrations ; the latter being placed 
in the form of notes at the bottom of the page. Each rule is ex¬ 
emplified by one wrought example ; and the most of them by 
several unwrought examples, with the answers annexed. 

In the laying out and dividing of land, which forms the most 
difficult part of surveying, a variety of problems is introduced, 
adapted to the cases most likely to occur in practice. This part 
of the subject, however, presents such a great variety of cases, 
that we should in vain attempt to give rules that would apply to 
all of them. It cannot therefore be too strongly recommended to 
every one, who has the opportunity, to make himself well ac¬ 
quainted with Geometry, and also with Algebra, previous to en¬ 
tering on the study of Surveying. Furnished with these useful 
auxiliaries, and acquainted with the principles of the science, the 
practitioner will be able to perform, with ease, any thing likely 
to occur in his practice. 

The compiler thinks proper to acknowledge, that in the ar¬ 
rangement of the work, he availed himself of the advice of his 
learned preceptor and friend, E. Lewis of New-Garden; and that 
several of the demonstrations were furnished by him. 











f 














. • 

ADVERTISEMENT 

TO THE FOURTH EDITION. 

■ 1 m { 

In preparing this edition for the press, several alter- 
ations have been made, which, it is believed, will be 
found to be real improvements. A number of new Prob¬ 
lems has been introduced, and a more methodical ar¬ 
rangement of the whole has been adopted. Instead of 
three different rules for calculating the content of a Sur¬ 
vey, one general rule, including these, is now given. It 

* 

may be further added, that the rules for solving several 
of the problems in Division of Land, have been consi¬ 
derably simplified. The Mathematical Tables have 
been Stereotyped after carefully revising them and com¬ 
paring them with the most correct European Editions. 

THE AUTHOR. 

Burlington, N. J. } 

Smo. 23rd. 1825. $ 










CONTENTS! 




Page. 

Logarithms, - -- -- - - -- -- 9 

Geometrical Definitions, - 25 

Geometrical Problems, - 29 

Plane Trigonometry, - - - - 35 

Application of Plane Trigonometry to the Mensuration of Distances and 

Heights, . 68 

Practical Questions, - 78 

Dimensions of a Survey, - 81 

Supplying Omissions in the dimensions of a Survey, - - - 107 

Problems for finding the Content of Land, - - - - - 118 

Laying out and dividing Land, ------- 163 

Variation of the Compass,.- 202 

Miscellaneous Questions, ------- - 213 






EXPLANATION 


OP THE 


CHARACTERS USED IN THIS WORK. 


X 


+ signifies plus, or addition. 

— minus , or subtraction. 

/ 

multiplication, 
division. 

: proportion, 

equality, 
square root. 

difference between two quantities when 
it is not known which is the greater. 


v/ 

(A 










OF LOGARITHMS. 







Logarithms are a series of numbers so contrived, 
that by them the work of multiplication is performed 
by addition, and that of division by subtraction. 

If a series of numbers in arithmetical progression be 
placed as indices, or exponants, to a series of numbers 
in geometrical progression, the sum or difference of any 
two of the former, will answer to the product or quo¬ 
tient of the two corresponding terms of the latter. 
Thus, 

0. 1.2. 3. 4. 5. 6. 7. &c. arith. series, or indices. 

# ' 

1. 2. 4. 8. 16. 32. 64. 128. &c. geom. series. 

Now 2+3=5. also 7—3=4. 

And 4x8=32. and 128-^-8=16 

. • 

Therefore the arithmetical series, or indices, have 
the same properties as logarithms; and these proper¬ 
ties hold true, whatever may be fche ratio of the geo¬ 
metrical series. 

There may, therefore, be as many different systems 
of logarithms, as there can be taken .different geome¬ 
trical series, having unity for the first term. But the 
most convenient system is that in which the ratio of the 

geometrical series is 10; and this is the one in com- 
B 




10 




LOGARITHMS. 


mon use. Thus, 

0. 1. 2. 3. 4. 5. &c. indices or logar. 

1. 10. 100. 1000. 10000. 100000. &c. natural numbers. 

In this system the log. of 1. is 0, # the log. of TO is 
1. the log. of 100, is 2, &c. Hence it is plain that the 
log. of any number between 1 and 10, will be expressed 
by a decimal, the log. of any number between 10 and 
100, by 1 and a decimal, the log. of any number be¬ 
tween 100 and 1000, by 2 and a decimal, &c. 

The numbers, 0,1, 2, 3, &c. that stand before the 
decimal part of logarithms, are called indices, and are 
always less by unity, than the number of figures in the 
integral part of the corresponding natural number. 

The index of the logarithm of a number, consisting 
in whole, or in part of integers, is affirmative; but if the 
number be a decimal, the index is negative, and is mark¬ 
ed by a negative sign (—) placed either before or 
above it. If the first significant figure of the decimal 
be adjacent to the decimal point, the index is, —1, or 1; 
if there be one cipher between them, the index is —2, or 
2; if there be two ciphers between them, the index is 
—3, or 3, &c. 

The decimal parts of the logarithms of numbers, con¬ 
sisting of the same figures and in the same order, are 
the same, whether the number be integral, fractional, 
or mixed. This is illustrated as follows: 


* In every system the logarithm of 1 is 0. 


LOGARITHMS. 


11 


Number 18960 
1896 

189.6 

18.96 

1.896 
.1896 
.01896 
’ .001896 

.0001896 


Logarithm 4.27784 

3.27784 

2.27784 

1.27784 

0.27784 

—1.27784 

, r - . * « 

—2.27784 

—3.27784 

—4.27784 


Tlie method of finding logarithms in the tables, and 
of multiplying, dividing, &c. by them, is contained in 
the following problems. 


.h * 


y. 


PROBLEM I. 


To find the Logarithm of a given number. 


If the given number consists of one or two figures only, 
find it in the column marked No. in the first page of 
the table, and against it in the next column marked log . 
is the logarithm. Thus the log. of 7 will be found 
0.84510, and the log. of 85 will be found 1.92942. 

But if the given number be either wholly or in part 
decimal, the index must be changed accordingly. Ob¬ 
serving that the index must always be one less than the 
number of figures in the integral part of the given num¬ 
ber; also, when the given number is wholly a decimal, 
the index is negative, and must be one more than the 
number of the ciphers between the decimal point and 
first significant figure on the left hand. Thus the log. 
of .7 is —1.84510, and the log. of .0085 is —3.92942. 

. 


If the given number consists of three figures, find it 
in one of the other pages of the table, in the column 
marked No. and against it, in the next column, is the 


12 


LOGARITHMS. 


decimal part of the logarithm. The index must be 
placed before it agreeably to the above observation. 
Thus the log. of 421 is 2.62428, the log. of 4.21 is 
0.62428, and the log. of .0421 is —2.62428. 

If the given number consists of four figures, find the 
three left hand figures in the column marked No. as be¬ 
fore, and the remaining, or right hand figure at the top 
of the table; in the column under this figure, and against 
the other three, is the decimal part of the logarithm. 
Thus the log. of 5163 is 3.71290, and the log. of .6387 
is —1.80530. 


If the given number consist of five or six figures, find 
the logarithm of the four left hand figures as before; 
then take the difference between this logarithm and the 
next greater in the table. Multiply this difference by 
the remaining figure or figures of the given number, and 
cut off one or two figures to the right hand of the pro¬ 
duct, according as the multiplier consists of one or 
two figures; then add the remaining figure or figures of 
the product to the logarithm first taken out of the table, 
and the sum will be the logarithm required. Thus, let 
it be required to find the logarithm of 59686; then, 


Logarithm of 5968 is 
The next greater log. is 

Difference 
Remaining figure 

Product - 

To ... 
Add 

Decimal part of the log. 


- 77583 

- 77590 


7 

6 


4,2 

- 77583 
4 


- 77587 





LOGARITHMS. 


13 


\ 


The natural number consisting of five integers, the 
index must be 4 ; therefore the log. of 59686 is 4.77587. 

■ 

Again, let it be required to find the log. of .0131755; 
then, 


Logarithm of 1317 is 

- 11959 

The next greater log. is - 

\ 

- 11991 

, % 

Difference - 

32 

I") • • /» 

Remaining figures - 

% i • • 

55 

• i 

Product - 

- 17,60 

To - 

11959 

Add 

18* 

Decimal part of the log. - 

- 11977 

/ 

As the given number is a decimal, and has one ci- 

pher between the decimal point 

and first significant 

figure, the index must be —2; therefore the log. of 

.0131755 is —2.11977. 

j 

Examples. 

1. Required the log. of 4.3 

Am. 0.63347 

2. Required the log. of 7986 

Ans. 3.90233 

3. Required the log. of .3754 

Am. -1.57449 

4. Required the log. of 596.87 

Am. 2.77588 

5. Required the log. of 785925 

Ans. 5.79538 

6. Required the log. of 6543900 

Ans. 6.81583 

7. Required the log. of .0027863 

Ans. -3.44503 


* Because 17.6 is nearer 18 than 17. 








14 


LOGARITHMS. 


PROBLEM II. 

i 

To find the natural number corresponding to a given 

If four figures only be required in the answer, look 
in the table for the decimal part of the given logarithm, 
and if it cannot be found exactly, take the one nearest 
to it, whether greater or less ; then the three figures 
in the first column, marked No. which are in a line with 
the logarithm found, together with the figure at the top 
of the table directly above it, will form the number re¬ 
quired. Observing, that when the index of the given 
logarithm is affirmative, the integers in the number 
found must be one more than the number expressed by 
the index; but when the index of the given logarithm is 
negative, the number found will be wholly a decimal, 
and must have one cypher less placed between the de¬ 
cimal point and first.significant figure on the left hand, 
than the number expressed by the index. Thus the na¬ 
tural number corresponding to the logarithm 2.90233 
is 798.6, the natural number corresponding to the loga¬ 
rithm 3.77055 is 5896, and the natural number corres¬ 
ponding to the logarithm —3.36361 is .00231. 

If the exact logarithm be found in the table, and the 
figures in the number corresponding do not exceed the 
index by one, annex ciphers to the right hand till they 
do. Thus the natural number corresponding to the lo¬ 
garithm 6.64068 is 4372000. 

. t 

If five or six figures be required in the answer, find, 
in the table, the logarithm next less than the given one, 
and take out the four figures answering to it as before. 
Subtract this logarithm from the next greater in the 
table, and also from the given logarithm; to the latter 
difference annex one or two ciphers, according as five 



LOGARITHMS. 


15 


or six figures are required, and divide the number thus 
produced, by the former difference; annex the quotient 
to the right hand of the four figures already found, and 
it will give the natural number required. 

Thus let it be required to find the natural number 
corresponding to the logarithm 2.53899 true to five fi¬ 
gures ; then, 

t '' • . ■ ■ 

w j " ' . / 

Given logarithm - .53899 

Next less - - - .53895 the natural number 

-corresponding is 3459. 

Diff. with one cipher annexed 40 

„ 'j s * , " i 

Next less log. - - .53895 
Next greater - - - .53908 

Difference 13 

Divide 40 by 13 and the quotient will be 3, which an¬ 
nexed to .the right hand of 3459, the four figures al¬ 
ready found, makes 34593; therefore as the index is 2, 
the required natural number is 345.93. 

Again let it be required to find the natural number 
corresponding to the logarithm 4.59859, true to six 
figures; then, 

Given logarithm - - .59859 

Next less - - - - .59857, the natural number an- 

-swering to it is 3968. 

Diff. with two ciphers annexed 200 

t. ' , • . ■ " ■ ; . . , 

Next less log. - - - 59857 

Next greater - - - 59868 

Difference - - - - 11 

* * 

Divide 200 by 11, and the quotient will be 18, which 
annexed to the right hand of 3968, the four figures al- 






16 


LOGARITHMS. 


ready found, makes 396818; therefore as the index is 4, 
the required natural number is 39681.8. 

EXAMPLES. 

1. Required the natural number answering to the lo¬ 
garithm 1.88030. Ans . 75.91. 

2. Required the natural number answering to the lo¬ 
garithm 5.37081. Ans. 234861. 

“ 3. Required the natural number answering to the lo¬ 
garithm 3.11977. Ans. 1317.56. 

4. Required the natural number answering to the lo¬ 
garithm -2.97435. Ans. .094265. 


PROBLEM III. 

To multiply numbers by means of logarithms. 

Case 1 . —When all the factors are whole or mixed 


numbers. 


t 


• >♦ 


RULE. 


Add together the logarithms of the factors, and the 
sum will be the logarithm of the product. 


EXAMPLES. 


1. Required the product of 84 by 56. 

Logarithm of 84 is 1.92428 


o 

Do. 


of 56 


is 

is 


1.74819 


Product 4704 


Sum 3.67247 


2. Required the continued product of 17.3,1.907 and 


34 . 


Logarithm of 17.3 is 1.23805 
Do. 1.907 is 0.28035 

Do. 34. is 1.53148 


Product 1121.71 


Sum 3.04988 




LOGARITHMS. 


17 


3. Find by logarithms the product of 76.5 by 5.5. 
Jins. 420.75. 

4. Find by logarithms the continued product of 
42.35, 1.7364 and 1.76. Arts. 129.424. 

Case 2.— When some or all of the factors are decimal 
numbers. 

+ i 


RULE. 


Add the decimal parts of the logarithms as before, 
and if there be any to carry from the decimal part, add 
it to the affirmative index or indices, or else subtract 
it from the negative. 

t 

t i 

Then add the indices together, when they are all 
of the same kind, that is, all affirmative or all negative; 
but when they are of different kinds, take the difference 
between the sums of the affirmative and negative ones, 
and prefix the sign of the greater. 

Note .—When the index is affirmative, it is not neces- 
sary to place any sign before it; but when it is nega¬ 
tive, the sign must not be omitted. 


EXAMPLES. 

t , • * j \ i . . * I. . 

1. Required the continued product of 349.17, 25.43, 


.93521 and .00576. 

Logarithm of 349.17 
Do. 25.43 

Do. {- .93521 
Do. .00576 

/ 

Product 47.83 


is 2.54303 
is 1.40535 
is -1.97090 
is -3.76042 





Sum 1.67970 







1 8 


LOGARITHMS. 


In this example there is 2 to carry from the decimal 
part of the logarithms, which added to 3, the sum of 
the affirmative indices, makes 5; from this taking 4, 
the sum of the negative indices, the remainder is 1, 
which is the index of the sum of the logarithms, and is 
affirmative, because the sum of the affirmative indices 
together with the number carried, exceeds the sum of 
the negative indices. 


2. Required the continued product of .0839, .7536, 
and .003179. / - . B 

Logarithm of .0839 is -2.92376 
Do. .7536 is -1.87714 
Do. .003179 is -3.50229 

Product .000201 Sum -4.30319 

In this example there is 2 to carry from the decimal 
part of the logarithms, which subtracted from 6, the 
sum of the negative indices, leaves 4, which is the in- 
dex of the sum of the logarithms, and is negative, be¬ 
cause the sum of the negative indices is the greater. 



3. Required the continued product of 13.19, .3765, 
and .00415. Ans. .02061. 

4. Required the continued product of 343,1.794,5.41 
and ,019. Ans . 63.25. 


PROBLEM IV. 


To divide numbers by means of Logarithms . 

Case 1 . —When the dividend and divisor are both 
whole or mixed numbers. 



LOGARITHMS. 


10 


\ 

RULE. 

Prom the logarithm of the dividend, subtract the lo¬ 
garithm of the divisor, the remainder will be the loga¬ 
rithm of the quotient. 

Note .—When the divisor exceeds the dividend, the 
question must be wrought by the rule given in the next 
case. 

, iSj 


EXAMPLES. 

]. Required the quotient of 3450 divided by 23. 

* : c • , 

Logarithm of 3450 is 3.53782 

Do. 23 is 1.36173 

jr i 

>’■ ■ 

Quotient 150 Remainder 2.17609 

2. Required the quotient of 420.75 divided by 76.5. 

Ans. 5.5. 

3. Required the quotient of 37.1542 divided by 

1.73958. Ans. 21.3585. 

Case 2.—When the dividend or divisor, or both of 
them, are decimal numbers. 

t v ^ T 

RULE. 

Subtract the decimal parts of the logarithms as be¬ 
fore, and if 1 be borrowed in the left hand place of the 
decimal part, add it to the index of the divisor when 
that index is affirmative, but subtract it when negative. 

Then conceive the sign of the index of the divisor 
changed from affirmative to negative, or from negative 
to affirmative; aftd if, when changed, it be of the same 
name with that of the dividend, add the indices to- 



20 


LOGARITHMS. 


gether; but if it be of a different name, take the differ¬ 
ence of the indices and prefix the sign of the greater. 

EXAMPLES. 

> 

1. Required the quotient of .7591 divided by 32.147. 

Logarithm of .7591 is -1.88030 
Do. 32.147 is 1.50714 

, f % 

- ■■ . 

Quotient .02361 Remain. -2.37316 

In this example the index of the divisor, with its sign 
changed, is —1, which added to —1, the index of the 
dividend, makes —2, for the index of the quotient. 

• * / 

2. Required the quotient of .63153 divided by .00917. 

\ * * i 

Logarithm of .63153 is -1.80039 
Do. .00917 is -3.96237 


Quotient 68.8683 Remain. 1.83802. 

In this example there is 1 to carry from the decimal 
part of the logarithm, which subtracted from —3, the 
index of the divisor, leaves —2; this, with its sign chan¬ 
ged, is +2; from which subtracting 1, the index of the 
dividend, the remainder is I, and is affirmative, because 
the affirmative index is the greater. 

3. Required the quotient of 13.921 divided by 7965.13. 

Logarithm of 13.921 is 1.14367 
Do. 7965.13 is 3.90125 




Quotient .001748 Remain. -^24242 





LOGARITHMS. 


21 


In this example there is 1 to carry from the decimal 
part of the logarithm, which added to 3, the index of 
the divisor, makes 4; this, with its sign changed, is, 
—4; from which subtracting 1, the index of the dividend, 
the remainder is —3. 

4. Required the quotient of 79.35 divided by .05178. 

Ans. 1532.46. 

5. Required the quotient of .5903 divided by .931. 

Ans, .63404. 

V. 

PROBLEM V. 

To involve a number to any power ; that is , to find the 
square , cube, 8{c. of a number logarithmically. 

> 

RULE. 

Multiply the logarithm of the given number by the 
index of the power, viz. by 2 for the square, by 3 for the 
cube, &c. and the product will be the logarithm of the 
power. 

V 

Note. —When the index of the logarithm is negative, 
if there be any to carry from the decimal part, instead 
of adding it to the product of the index and multiplier, 
subtract it, and the remainder will be the index of the 
logarithm of the power, and will always be negative. 

EXAMPLES. 

U c'l .1 'j • L 9 v 

1. Required the square of 317. 

Logarithm of 317 is 2.50106 

2 


Square 100489 5.00212 



22 


r 

LOGARITHMS. 

i 

2. Required the 5th power of 1.735. 

Logarithm of 1.735 is 0.23930 

5 

\ -■ 

5th power 15.7218 1.19650 

3. Required the cube of .08761. 

Logarithm of .08761. is -2.94255 

O 

3 

Cube .0006724 -4.82765 

4. Required the cube of 7.503. Ans. 422.37. 

5. Required the 7th power of .32513. Ans. .0003841. 

PROBLEM VI. 

To extract any root of a number logarithmically. 

RULE. 

/ 

Divide the logarithm of the given number by the in¬ 
dex of the root, that is, by 2 for the square root, by 3 
for the cube root/ &c. and the quotient will be the 
logarithm of the required root. 

Note .—When the index of the logarithm is negative, 
and does not exactly contain the divisor, increase the 
index by a number just sufficient to make it exactly divi¬ 
sible by it, and carry the units borrowed, as so many 
tens, to the left hand figure of the decimal part; then 
proceed with the division in the usual manner. 

A 1 







LOGARITHMS. 


23 


EXAMPLES. 

1. Required the cube root of 391.27. 

3) 

Logarithm of 391.27 is 2.59248 

t , - 

Cube root 7.314 0.86416 

I V ■ 

2. Required the square root of .08593. 

2 ) 

Logarithm of .08593 is —2.93414 


Square root .29314 —1.46707 

3. Required the cube root of .7596. 

3 ) 

Logarithm of .7596 is —1.88058 


Cube root .9124 —1.96019 

4. Required the cube root of .0000613. 

!;i.L: 3 ) 

Logarithm of .0000613 is —5.78746 


Cube root .03943 —2.59582 

5. Required the square root of 365. Ans. 19.105. 

6. Required the 5th root of .9563. Ans. .9911. 

7. Required the 4th root of .00079. Ans. .16765. 

Of the Arithmetical Complements of Logarithms. 

When it is required to subtract several logarithms 
from others, it will be more convenient to convert the 
subtraction into an addition, by writing down, instead 
of the logarithms to be subtracted, what each of them 
wants of 10.00000, which may readily be done, by writ- 






/ 


24 LOGARITHMS. 

ing down what the first figure, on the right hand, wants 
of 10, and what every other figure wants of 9; this re¬ 
mainder is called the Arithmetical Complement. Thus, if 
the logarithm be 2.53061, its arithmetical complement 
will be 7.46939. If one or more figures to the right 
hand be ciphers, write ciphers in their place, and take 
the first significant figure from 10, and the remaining 
figures from 9. Thus, if the logarithm be 4.61300, its 
*• arithmetical complement will be 5.38700. 

. < 

In any operation, where the arithmetical com¬ 
plements of logarithms are added to other logarithms, 
there must be as many tens subtracted from the sum, as 
there are arithmetical complements used. 

As an example, let it be required to divide the pro¬ 
duct of 76.4 and 35.84, by the product of 473.9 and 4.76. 


473.9 
4.76 - 

35.84 - 

76.4 

Quotient 1.214 


Ar. Co. 7.32431 
Ar. Co. 9.32239 

- log. 1.55437 

- log. 1.88309 


0.08416 





* V 














GEOMETRY. 


DEFINITIONS. 

* 

1. Geometry is that science wherein the properties 
of magnitude are considered. 

2. A point is that which has position, but not magni¬ 
tude. 

3. A line has length but not breadth. 

4. A straight, or right line, is the shortest line that 
can be drawn between any two points. 

5. A superficies or surface is that which has length 
and breadth, but not thickness. 

6. A plane superficies is that in which any two points 
being taken, the straight line which joins them lies whol¬ 
ly in that superficies. 

7. A plane rectilineal angle is the inclination of two 
straight lines to one another, which meet together, but 
are not in the same straight line, as a, Fig. 1. 

JVote .—When several angles are formed about the 
same point, as at b, Fig. 2, each particular angle is ex¬ 
pressed by three letters, whereof the middle letter shows 
the angular point, and the other two the lines that form 
the angle; thus, cbd or dbg signifies the angle formed 
by the lines cb and db. 

D 



26 


GEOMETRY. 


8. The magnitude of an angle depends on the incli¬ 
nation which the lines that form it have to each other, 
and not on the length of those lines. Thus the angle 
dee is greater than the angle abc, Fig. 3. 

9. When a straight line stands on another straight 
line so as to incline to neither side, but makes the angles 
on each side equal, then each of those angles is called 
alright angle, and the line which stands on the other is 
said to be perpendicular to it. Thus adc and bdc are 
right angles, and the line cd is perpendicular to ab, Fig. 4. 

10. An acute angle is that which is less than a right 
angle, as bde, Fig. 4. 

11. An obtuse angle is that which is greater than a 
right angle, as ade, Fig. 4. 

12. Parallel straight lines are those which are in the 
same plane, and which, being produced ever so far 
both ways, do not meet, as ab, cd, Fig. 5. 

13. A figure is a space bounded by one or more lines. 

14. A plane triangle is a figure bounded by three 
straight lines, as abc, Fig. 6. 

15. An equilateral triangle has its three sides equal 
to each other, as a, Fig. 7. 

16. An isosceles triangle has only two of its sides 
equal, as b, Fig. 8. 

17. A scalene triangle has three unequal sides, as 
abc, Fig. 6. 

18. A right angled triangle has one right angle, as 
abc, Fig. 9; in which the side ac opposite to the right 
angle is called the hypothenuse. 



GEOMETRY. 


27 


19. An obtuse angled triangle has one obtuse angle 
as c, Fig. 10. 

20. An acute angled triangle has all its angles acute, 
as abc, Fig. 6. 

21. Acute and obtuse angled triangles are called 
oblique angled triangles. 

- r 

22. Any plane figure bounded by four right lines, is 
called a quadrilateral. 

23. Any quadrilateral, whose opposite sides are paral¬ 
lel, is called a parallelogram, as d, Fig. 11. 

• 

24. A parallelogram, whose angles are all right 
angles, is called a rectangle, as e, Fig. 12. 

25. A parallelogram whose sides are all equal, and 
angles right, is called a square, as f, Fig. 13. 

26. A rhomboides is a parallelogram, whose op¬ 
posite sides are equal and angles oblique, as d, Fig. 11. 

27. A rhombus is a parallelogram, whose sides are 
all equal and angles oblique, as g, Fig. 14. 

28. Any quadrilateral figure that is not a parallelo¬ 
gram, is called a trapezium. 

29. A trapezium that has two parallel sides is called 
a trapezoid. 

30. A right line joining any two opposite angles of a 
quadrilateral figure, is called a diagonal. 

31. That side upon which any parallelogram, or 
triangle is supposed to stand, is called the base; and 
the perpendicular falling thereon from the opposite 


28 


GEOMETRY. 


angle is called the altitude of the parallelogram, or 
triangle. Thus ad is the base of the parallelogram 
abec, or triangle abc, and cd is the altitude. Fig. 15. 

32. All plane figures contained under more than 
four sides, are called polygons; of which those having 
five sides, are called pentagons ; those having six sides, 
hexagons, and so on. 

%• • 

33. A regular polygon is one whose angles, as well 
as sides, are all equal. 

. ' \ 

34. A circle is a plane figure, bounded by one curve 
line called the circumference or periphery, every part 
of which is equally distant from a’certain point within 
the circle; and this point is called the centre, Fig. 16. 

35. The radius of a circle is a straight line drawn 
from the centre to the circumference, as cb, Fig 17. 

i * 

36. The diameter of a circle is a straight line drawn 
through the centre, and terminated both ways by the 
circumference, as ae, Fig. 17. It divides the circle into 

two equal parts, called semicircles. 

< * 

37. A quadrant is one quarter of a circle, as acb, Fig. 

17. 

Note. —The fourth part of the circumference of a 
circle is also called a quadrant. 

38. A segment of a circle is the figure contained by 
a right line, and the part of the circumference it cuts 
off: thus aeba and aeda are segments of the circle abed, 
Fig. 16. 

39. An arc of a circle is any part of the circum¬ 
ference; as ad or de, Fig. 17. 


GEOMETRY. 29 

40. Ratio is a mutual relation between two quan¬ 
tities of the same kind with respect to magnitude. 

j 

Note. —A ratio is generally expressed, either by two 
numbers or by two right lines. 

41. When two quantities have the same ratio as two 
other quantities, the four quantities taken in order are 
called proportionals; and the last is said to be a fourth 
proportional to the other three. 

% 

42. When three quantities of the same kind are such 
that the first has to the second the same ratio which 
the second has to the third, the third is called a third 
proportional to the first and second, and the second is 
called a mean proportional between the first and third. 


GEOMETRICAL PROBLEMS. 
PROBLEM I. 

To bisect a right line , ab, Fig 18. 

Open the dividers to any distance more than half the 
line ab, and with one foot in a, describe the arc cfd ; 
with the same opening, and one foot in b, describe the 
arc cgd, meeting the first arc in c and p; from c to d 
draw the right line cd, cutting ab in e, which will be 
equally distant from a and b. 

PROBLEM II. 

At a given point a, in a right line ef, to erect a perpen¬ 
dicular , Fig. 19. 

From tiie point a, lay off on each side, the equal dis- 




30 GEOMETRICAL PROBLEMS. 

tances ac, ad; from c and d, as centres, with any 
radius greater than ac or ad, describe two arcs in¬ 
tersecting each other in b ; from a to b, draw the line 
ab, which will be the perpendicular required. 

PROBLEM III. 

To raise a perpendicular on the end b of a light line ab, Fig. 

20 . 'Wt 

Take any point d not in the line ab, and with the 
distance from d to b, describe a circle cutting ab in e ; 
from e through d draw the right line edc, cutting the 
periphery in c, and join cb, which will be perpendicular 

to AB. 

PROBLEM IV. 

To let fall a perpendicular upon a given line bc from a 

given point a, without it , Fig. 21. 

In the line bc take any point d, and with it as a cen¬ 
tre and distant da describe an arc age, cutting bc in g ; 
with g as centre, and distance ga, describe an arc cut- 
ing age in e, and from a to e draw the line afe ; then 
af will be perpendicular to ab. 

PROBLEM V. 

Through a given point a to draiv a right line ab, parallel to 

a given right line cd, Fig. 22. 

From the point a to any point f, in the line cd, draw 
the right line af ; with f as a centre and distance fa, 
describe the arc ae, and with the same distance and 
centre a describe the arc fg ; make fb equal to ae, 
and through a and b draw the line ab, and it will bc 
parallel to cd. 


I 


GEOMETRICAL PROBLEMS. 31 

PROBLEM VI. 

At a given point b, in a given right line lg, to make an 
angle equal to a given angle a, Fig. 23. 

With the centre a and any distance ae, describe the 
arc de, and with the same distance and centre b de¬ 
scribe the arc fg ; make hg equal to de, and through b 
and h draw the line bh; then will the angle hbg be 
equal to the angle a. 

PROBLEM VII. 

To bisect any right lined angle bac, Fig, 24. 

In the lines ab and ac, from the point a, set off equal 
distances ad and ae ; with the centres d and e and any 
distance more than half de, describe two arcs cutting 
each other in f ; from a through f draw the line ag, 
and it will bisect the angle bac. 

PROBLEM VIII. 

r 

To describe a triangle that shall have its sides respectively 
equal to three right lines d, e, and f, of which any two must 
be together greater than the third , Fig 25. 

SrT 

Make ab equal to d ; with the centre a and distance 
equal to e, describe an arc, and with the centre b and 
distance equal to f describe another arc, cutting the 
former in c; draw ac and bc, and abc is the triangle 
required. 

PROBLEM IX. 

Upon a given line ab to describe a square , Fig 26. 

At the end b of the line ab, by Problem III. erect the 
perpendicular bc, and make it equal to ab ; with a and 
c as centres, and distance ab or bc describe two arcs 


/ 


32 


GEOMETRICAL PROBLEMS. 


cutting each other in d; draw ad and cd, then will abcd 
be the square required. 

PROBLEM X. 

To describe a circle that shall pass through the angular 
points, a, b, and c, of a triangle abc, Fig. 27. 

By Problem I. bisect any two of the sides, as ac, bc, 
by the perpendiculars de and fg ; the point h where they 
intersect each other will be the centre of the circle; with 
this centre, and the distance from it to either of the 
points a, b, or c, describe the circle. 

PROBLEM XI. 

To divide a given right line ab into any number of 

equal parts, Fig. 28. 

/ . I 

Draw the indefinite right line ap, making an angle 
with ab, also draw bq parallel to ap, in each of which, 
take as many equal parts am, mn, &c. Bo, on, &c. as 
the line ab is to be divided into; then draw Mm, JYn, &c. 

i 

intersecting ab in e, f, &c. and it is done. 

PROBLEM XII. 

To make a plain diagonal scale, Fig. 29. 

Draw eleven lines parallel to, and equidistant from 
each other; cut them at right angles by the equidistant 
lines bc; ef; 1, 9; 2, 7 ; &c. then will bc, &c. be divided 
into ten equal parts; divide the lines eb, and fc, each 
into ten equal parts, and from the points of division on 
the line eb, draw diagonals to the points of division on 
the line fc : thus join e and the first division on fc, the 

first division on eb, and the second on fc, &c. 

* 

Note. —Diagonal scales serve to take off dimensions 
or numbers of three figures. If the first large divisions 
be units, the second set of divisions, along eb, will be 


\ 


GEOMETRICAL PROBLEMS. 33 

% 

% 

10th parts; and the divisions in the altitude, along bc, 
will be 100th parts. If he be tens, eb will be units, and 
bc will be tenth parts. If he be hundreds, be will be 
tens, and bc units. And so on, each set of divisions 
being tenth parts of the former ones. 

For example, suppose it were required to take off 242 
from the scale. Extend the dividers from e to 2 towards 
h ; and with one leg fixed in the point 2, extend the other 
till it reaches 4 in the line eb ; move one leg of the di¬ 
viders along the line 2, 7, and the other along the line 
4, till they come to the line marked 2, in the line bc, 
and that will give the extent required. 

PROBLEM XIII. 


To find a third proportional to two given right lines , 

a and b. 

Draw two right lines, cd, ce 
containing any angle; make cf 
equal a, and cg, ch each equal 
b ; join fg and draw hl paral¬ 
lel to it: then will cl be the 
third proportional required. 



PROBLEM XIV. 


To find a fourth proportional to three given right lines , 

a, b and c. 




Draw two right lines, de, df 
containing any angle; make dg 
equal a, dh equal b, and dl 
equal c ; join gh and draw lm 
parallel to it: dm will be a 
fourth proportional to a, b, and 
c. 


A 

33 

C 


2 ) 



K 


F 


E 


H M 












34 


GEOMETRICAL PROBLEMS. 


PROBLEM XV. 

To find a mean proportional between two given right lines 

a and b. 

Draw any right line ce and in 
it take cd equal a, and de equal 
b; bisect ce in f, and with the 
centre f and radius fc or fe 
describe the semicircle cge; 
draw dg perpendicular to ce : 
then dg will be a mean propor¬ 
tional between a and b. 

PROBLEM XVI. 

To divide a given right line ab into two parts that 
shall have the same ratio to each other as two given lines c 
and d. 

Draw ae making an angle 
with ab; in ae take af equal ^ 
c and fe equal d: join eb and 
draw fg parallel to it; then ag 
will have to gb the same ratio A 
that c has to d. 

PROBLEM XVII. 


is 




To divide a given right line ab into two parts in the 
point d, so that ad may be to db in the ratio of two given 
numbers m and n. For example , let m— 3, and n— 4. 


Draw ac making any angle with ab ; take 
the number m from any convenient scale 
of equal parts, and lay it on ac, from a to e ; 
and take the number n from the same scale, 
and lay it from e to c; join cb and draw ed 
parallel to it; then ab will be divided as re¬ 
quired. 













PLANE TRIGONOMETRY. 


DEFINITIONS. 

1. Plane Trigonometry is the art by which, when 
any three parts of a plane triangle, except the three 
angles, are given, the others are determined. 

2. The periphery of every circle is supposed to be di¬ 
vided into 360 equal parts, called degrees; each degree 
into 60 equal parts, called minutes; and each minute 
into 60 equal parts, called seconds, &c. 

3. The measure of an angle is the arc of a circle, con¬ 
tained between the two lines that form the angle, the 
angular point being the centre; thus the angle abc, 
Fig. 30, is measured by the arc de, and contains the 
same number of degrees that the arc does. The mea¬ 
sure of aright angle is therefore 90 degrees; for dh, Fig. 
31, which measures the right angle dch, is one fourth 
part of the circumference, or 90 degrees. 

Note .—The degrees, minutes, seconds, &c. contained 
in any arc, or angle, are written in this manner, 50° 18' 
35"; which signifies that the given arc or angle contains 
50 degrees 18 minutes and 35 seconds. 

V 1 

4. The complement of an arc, or of an angle, is what 
it wants of 90°; and the supplement of an arc, or of an 
angle, is what it wants of 180°. 





36 


PLANE TRIGONOMETRY 


5. The chord of an arc, is a right line drawn from 
one extremity of the arc to the other: thus the line be 
is the chord of the arc bae or bde, 31. 

6. The sine of an arc, is a right line drawn from one 
extremity of the arc, perpendicular to the diameter 
which passes through the other extremity: thus bf is the 
sine of the arc ab or bd, Fig. 31. 

7. The cosine of an arc, is that part of the diameter 
which is intercepted between the sine and the centre: 
thus cf is the cosine of the arc ab, and is equal to bi, 
the sine of its complement hb, Fig. 31. 

8. The versed sine of an arc, is that part of the dia¬ 
meter which is intercepted between the sine and the arc: 
thus af is the versed sine of ab; and df of db, Fig. 31. 

9. The tangent of an arc, is a right line touching the 
circle in one end of the arc, being perpendicular to the 
diameter which passes through that end, and is termina¬ 
ted by a right line drawn from the centre through the 
other end: thus ag is the tangent of the arc ab, Fig. 31. 

10. The secant of an arc, is the right line drawn from 
the centre and terminating the tangent; thus cg is the 
secant of ab, Fio*. 31. 

11. The cotangent of an arc, is the tangent of the 
complement of that arc; thus hk is the cotangent of ab, 
Fig. 31. 


12. The cosecant of an arc, is the secant of the com¬ 
plement ol that arc ; thus ck is the cosecant of ab, Fig. 


31 . 



PLANE TRIGONOMETRY. 


37 


13. The sine, cosine, &c. of an angle is the same as 
the sine, cosine, &c. of the arc that measures the angle. 

PROBLEM 1. 

M , ^ ■ * * 

To construct the lines of cords, sines , tangents , and secants , 

to any radius. Fig. 32. 

* 

Describe a semicircle with any convenient radius cb ; 
from the centre c draw cd perpendicular to ab and 
produce it to f ; draw be parallel to cp and join ad. 

Divide the arc ad into nine equal parts, as a 10; 10, 20, 
&c. and with one foot of the dividers in a, transfer 
the distances a, 10; a, 20, &c. to the right line ad; 
then will ad be a line of chords constructed to every ten 
degrees. 

Divide bd into nine equal parts, and from the points 
of division, 10, 20, 30, &c. draw lines parallel to cb, 
and meeting cd in 10, 20, 30, &c. and cd will be a 
line of sines. 

From the centre c, through the divisions of the arc 
bd, draw lines meeting be, in 10, 20, 30, &c. and be 
will be a line of tangents. 

With one foot of the dividers in c transfer the dis¬ 
tances from c to 10, 20, &c. in the line be, to the line 
cf, which will then be a line of secants. 

By dividing the arcs ad and bd each into 90 equal 
parts, and proceeding as above, the lines of chords, 
sines, &c. may be constructed to every degree of the 
quadrant. 


38 


PLANE TRIGONOMETRY, 


\ * 

PROBLEM II. 

At a given point a in a given right line ab, to make an 
angle of any proposed number of degrees , suppose 38 degrees. 
Fig. 33. 

With the centre a, and a radius equal to 60 degrees, 
taken from a scale of chords, describe an arc, cutting 
ab in m ; from the same scale of chords, take 38 degrees 
and apply it to the arc from m to w, and from a through 
n draw the line ac, then will the angle a contain 38 
degrees. 

JVote .— Angles of more than 90 degrees are usually 
taken off at twice. 

PROBLEM III. 

To measure a given angle a. Fig. 34. 

Describe the arc mn with the chord of 60 degrees, as 
in the last problem. Take the arc mn between the divi¬ 
ders, and that extent applied to the scale of chords, 
will show the degrees in the given angle. 

JYote. —When the distance mn exceeds 90 degrees, it 
must be taken off at twice, as before. 

• .. . . ’" • < 


% 



PLANE TRIGONOMETRY. 


39 


OF THE TABLE 

' :• K:* iv ■ f 

OP 

LOGARITHMIC OR ARTIFICIAL SINES, TANGENTS, &c. 

/ 

This table contains the logarithms of the sine, tan¬ 
gent, &c. to every degree and minute of the quadrant, 
the radius being 10000000000, and consequently its lo¬ 
garithm 10. 

Let the radius cb, Fig. 32, be supposed to consist of 
10000000000 equal parts as above, and let the qua¬ 
drant db be divided into 5400 equal arcs, each of these 
will therefore contain T; and if from the several points 
of division in the quadrant, right lines be drawn per¬ 
pendicular to cb, the sine of every minute of the qua¬ 
drant to the radius cb will be exhibited. The lengths 
of these lines being computed and arranged in a table, 
constitute what is usually termed a table of natural sines. 
The logarithms of those numbers taken from a table of 
logarithms and properly arranged form the table of loga¬ 
rithmic or artificial sines. In like manner the logarithmic 
tangents and secants are to be understood. 

The method by which the sines are computed is too 
abstruse to be explained in this work, but a familiar ex¬ 
position of this subject as well as the construction of lo¬ 
garithms may be seen in Simson’s Trigonometry. 

To find , by the table , the sine , tangent , 8{c. of an arc or 

angle. 

i 

If the degrees in the given angle be less than 45, look 
for them at the top of the table, and for the minutes, in 


40 


PLANE TRIGONOMETRY. 


the left hand column; then in the column marked at the 
top of the table, sine, tangent, &c. and against the mi¬ 
nutes, is the sine, tangent, &c. required. If the degrees 
are more than 45, look for them at the bottom of the 
table, and for the minutes, in the right hand column; 
then in the column marked at the bottom of the table, 
sine, tangent, &c. and against the minutes, is the sine, 
tangent, &c. required. 

JYotc .—The sine of an angle and of its supplement 
being the same, if the given number of degrees be above 
90, subtract them from 180°, and find the sine of the 
remainder. 


1. Required the sine of 32° 27' 

2. Required the tangent of 57° 39 

3. What is the secant of 89° 31' 

4. What is the sine of 157° 43' 

To find the degrees and minutes corresponding to a given 

sine , tangent , &e. 

, * • 

Find, in the table, the nearest logarithm to the given 
one, and the degrees answering to it will be found at 
the top of the table, if the name be there, and the mi¬ 
nutes on the left hand; but if the name be at the bottom 
of the table, the degrees must be found at the bottom, 
and the minutes at the right hand. 






Jins. 9.72962. 
Am. 10.19832. 
Am. 12.G7388. 
Ans. 9.57885. 


EXAMPLES. 

1. Required the degrees and minutes in the angle 
whose sine is 9.64390. Jins. 26° 8'. 


PLANE TRIGONOMETRY. 


41 


2. Required the degrees and minutes in the angle 
whose tangent is 10.47464. jins. 71° 28'. 


ON GUNTER’S SCALE. 

Gunter’s Scale is an instrument by which, with a pair 
of dividers, the different cases in trigonometry, and 
many other problems, may be solved. 

It has on one side, a diagonal scale, and also the lines 
of chords, sines, tangents, and secants, with several 
others. 

On the other side there are several logarithmic lines as 
follow: 

The line of numbers marked JYum ., is numbered from 
the left hand of the scale towards the right, with 1, 2, 3, 
4, 5, 6, 7, 8, 9, 1, which stands in the middle of the 
scale; the numbers then go on 2, 3, 4, 5, 6, 7, 8, 9, 10, 
which stands at the right hand end of the scale. These 
two equal parts of the scale are similarly divided, the 
distances between the first 1, and the numbers 2, 3, 4, 
&c. being equal to the distances between the middle ], 
and the numbers 2, 3,4, &c. which follow it. The sub- 
divisions of the two parts of this line are likewise simi¬ 
lar, each primary division being divided into ten parts, 
distinguished by lines of about half the length of the 
primary divisions. 

The primary divisions on the second part of the scale, 

are estimated according to the value set upon the unit on 

the left hand of the scale: If the first 1 be considered 

as a unit, then the first 1, 2, 3, &c. stand for 1, 2, 3, &c. 

the middle 1 is 10, and the 2, 3, 4, &c. following stand 
F 


I 


42 PLANE TRIGONOMETRY. 

for 20, 30, 40, &c. and the ten at the right hand for 100, 
If the first 1 stand for 10, the first 2, 3, 4, &c. must be 
counted 20, 30, 40, &c. the middle 1 will be 100, the 
second 2,3,4, &c. will stand for 200, 300, 400, &c. and 
the 10 at the right hand for 1000. 

If the first 1 be considered as T V of a unit, the 2, 3, 
4, &c. following will be T 2 o, T V, A? &c. and the middle 1, 
and the 2, 3,4, &c. following will stand for 1, 2, 3,4, &c. 

The intermediate small divisions must be estimated 
according to the value set upon the primary divisions. 

Sines. —The line of sines, marked Sin., is numbered 
from the left hand of the scale toward the right, 1, 2, 3, 
4, &c. to 10, then 20, 30, 40, &c. to 90, where it termi¬ 
nates just opposite 10 on the line of numbers. 

Tangents .— The line of tangents, marked Tan., begins 
at the left hand, and is numbered 1 , 2, 3, &c. to 10, then 
20, 30, 40, 45, where there is a brass pin, just under 90 
in the line of sines; because the sine of 90° is equal to 
the tangent of 45°. From 45 it is numbered towards the 
left hand 50, 60, 70,80, &c. The tangent of acres above 
45° are therefore counted backward on the line, and are 
found at the same points of the line as the tangents of 
their complements. 

There are several other lines on this side of the scale, 
as Sine Rhumbs , Tangent Rhumbs , Versed Sines , &c.; but 
those described are sufficient for solving all the pro¬ 
blems in plane trigonometry. 

Remarks on Angles , Triangles , &c. 

1. If from a point d in a right line ab, one or more 
right lines be drawn on the same side of it, the angles 
thus formed at the point d will be together equal to two 


r 


PLANE TRIGONOMETRY. 43 

■ ■ f • JMk ^ " i 

right angles, or 180°; thus ade -j- edb ” two right angles, 
or 180°: also ADc+CDE-(-EDB=two right angles, or 180°. 
Fig. 35. 

2. Since the angles thus formed at the point d, on the 
other side of ab, would also be equal to two right angles, 
the sum of all the angles formed about a point is equal 
to four right angles or 360°. 

3. If two right lines cut one another, the opposite 
angles will be equal: thus aec=tbed and aed^ceb. Fig. 
36. 

i 

4. The sum of the three angles of a plane triangle is 
equal to two right angles, or 180°. 

5. If the sum of two angles of a triangle be subtracted 
from 180°, the remainder will be the third angle. 

6. If one angle of a triangle be subtracted from 180°, 
the remainder will be the sum of the other two angles. 

7. In right-angled triangles, if one of the acute angles 
be subtracted from 90°, the remainder will be the other 
acute angle. 

* 9 J 

8. The angles at the base of an isosceles triangle are 
equal to one another. 

i 

9. If one side of a triangle be produced, the external 
angle will be equal to the sum of the two internal and 
opposite angles: thus the external angle cbd, of the 
triangle abc, is equal to the sum of the internal and 
opposite angles a and c. Fig. 37. 




> * * - ' 

» f N r* 

44 PLANE TRIGONOMETRY. 

10. The angle at the centre of a circle is double of 
the angle at the circumference, upon the same base, that 
is upon the same part of the circumference: thus the 
angle bec is double of the angle bac. Fig. 38. 

11. The angles in the same segment of a circle are 

equal to one another : thus the angle bad is equal to the 
angle bed ; also the angle bcd is equal to the angle bfd. 
Fig. 39. i 

12. The angle in a semicircle is a right angle: thus 
the angle ecf, Fig. 45, is a right angle. 

13. This mark' placed on the sides or in the angles 
of a triangle, indicates that they are given; and this 
mark ° placed in the same way, indicates that they are 
required. 

PRACTICAL RULES FOR SOLVING ALL THE CASES OF 

PLAIN TRIGONOMETRY. 

» • 

CASE 1. 

The angles and one side of any plain triangle being given , 

the other sides. 

RULE. 

f • % 

VIluh • fi 1 / v ‘ , a 

As the sine of the angle opposite the given side, 

Is to the sine of the angle opposite the required side, 

So is the given side, 

To the required side.* 


* Demonstration. Let abc, Fig. 40, be any plane triangle; take bf=ac, 
and upon ab let fall the perpendiculars cd and fe, which will be the sines of 








PLANE TRIGONOMETRY. 


45 


Note 1.—The proportions in trigonometry are worked 
by logarithms : thus, from the sum of the logarithms of 
the second and third terms, subtract the logarithm of 
the first term, and the remainder will be the logarithm of 
the fourth term. 

2. The logarithmic sine of a right angle or 90° is 
10.00000, being the same as the logarithm of the ra= 
dius. 


EXAMPLES. 

1. In the triangle abc, there are given the angle a=. 
32° 15', the angle B=rll4°24', and consequently the 
angle c=33° 21' and the sides ab=:98; # required the 
sides, ac and bc. 

By Construction , Fig. 41. 

Make ab equal to 98 by a scale of equal parts, and 
draw ac, making the angle a =32° 15'; also make the 
angle b=114° 24' and produce bc, ac, till they meet in 
c, then is abc the triangle required; and ac measured 
by the same scale of equal parts, is 162, arid bc is 95. 


the angles a and b to the equal radii ac and bf. Now the triangles bdc and bef 
being similar, we have cd : fe : : bc : bf : or ac ; that is sin. a : sin. b : : bc : ac. 
In like manner it is proved, that sin. a : sin. c : : bc : ab. When one of the 
angles is obtuse, the demonstration is the same. Hence it appears, that in any 
plain triangle, the sides are to one another as the sines of their opposite angles. 


* This 93 may express so many feet, or yards, &c., and the other sides will 
be of the same denomination as the given. 




46 PLANE TRIGONOMETRY. 


By Calculation . 

As sine of the angle c 33° 21' - - 9.74017 


Is to sine of the angle b 114° 24' - - 9.95937 
So is ab 98 . 1.99123 

. r -— 

11.95060 

9.74017 


To ac 162.3 . 2.21043 


As sine ofc 33° 21' ----- 9.74017 


Is to sine of a 32° 15' - - - - - 9.72723 

So is ab 98 . 1.99123 


11.71846 

9.74017 


To bc 95.12 . 1.97829 


By Gunter's Scale. 

Extend the compasses, on the line of sines, from 
33° 21' to 65° 36' the supplement of the angle b; that 
extent will reach, on the line of numbers, from 98 to 162, 
the side ac. 

Extend the compasses from 33° 21' to 32° 15' on the 
line of sines; that extent will reach, on the line of num¬ 
bers, from 98 to 95, the side bc. 

2. In the right-angled triangle abc, are given the hy- 
pothenuse ac=480, and the angle a=53° 8'. To find 
the base ab and perpendicular bc. 












PLANE TRIGONOMETRY. 


47 


From 90° subtract the angle a = 53 ° 8'; the remain¬ 
der 36° 52' will be the angle c. The angle b, being a 
right angle, is 90°. 


By Construction , Fig. 42. 

This may be constructed as in the preceding exam¬ 
ple, or otherwise thus, 

Draw the line ab of any length, and draw ac making 
the angle a=53° 8'; make ac=480 by a scale of equal 
parts, and from c draw cb perpendicular to ab, then 
abc is the triangle required, ab, measured by the same 
scale of equal parts, will be 288, and bc will be 384. 


By Calculation. 

As sine of b 90°. 10.00000 

Is to sine of a 53° 8' - - - - 9.90311 

So is ac 480 . 2.68124 


12.58435 


To bc 384 . 2.58435 

As sine of b 90° ----- 10.00000 

Is to sine of c 36° 52' - - - 9.77812 

So is ac 480 ------ 2.68124 

12.45936 

To ab 288 . 2.45936 














48 


✓ 


PLANE TRIGONOMETRY. 


By Gunter’s Scale. 

Extend the compasses, on the line of sines, from 90° 
to 53° 8', that extent will reach, on the line of numbers, 
from 480 to 384 the perpendicular bc. 

Extend the compasses, on the line of sines, from 90° 
to 36° 52', the complement of the angle a ; that extent 
will reach, on the line of numbers, from 480 to 288, the 
base ab. 

3. In the triangle abc, are given the angle a=79° 23', 
the angle b=54° 22', and the side bc=t125; required 
ac and ab. Jins. ac= 103.4, and ab=91.87. 

4. In a right-angled triangle, there are given the 
angle a=56° 48', and the base ab= 53.66, to find the 
perpendicular bc and hypothenuse ac. Ans. bc=82 
and ac— 98. 

5. In the right-angled triangle abc, are given the 
angle a=39° 10', and the perpendicular bc=407.37, to 
find the base ab and hypothenuse ac. Ans. ab= 500.1, 
and ac=645. 

CASE 2. 

Two sides and an angle opposite one of them being given , to 
find the other angles and side. 

RULE. 

As the side opposite the given angle, 

Is to the other given side, 

So is the sine of the angle opposite the former, 

To the sine of the angle opposite the latter.* 


* This is evident from the demonstration of the rule in the preceding case. 






PLANK TRIGONOMETRY. 49 

4 

Add the angle thus found to the given angle, and sub¬ 
tract their sum from 180 °, the remainder will be the 
third angle. 

After finding the angles, the other side may be found 
by Case 1. 

Note. —The angle found by this rule is sometimes am¬ 
biguous, for the operation only gives the sine of the 
angle, not the angle itself; and the sine of every angle is 
also the sine of its supplement. 

When the side opposite the given angle is equal to, 
or greater than the other given side, then the angle op¬ 
posite that other given side is always acute ; but when 
this is not the case, that angle may be either acute or 
obtuse, and is consequently ambiguous. 

EXAMPLES. 

1. In the triangle abc, are given the angle c = 33° 
21', the side ab=.98 and the side bc=.7912 ; required 
the angles a and b, and the side bc. 

By Construction , Fig. 43. 

Make bc— .7912 by a scale of equal parts, and draw 
ca, making the angle c—33° 21'; with the side ab= 
.98, in the compasses, taken from the same scale of 
equal parts, and b as a centre, describe the arc ab , cut¬ 
ting ac in the point a, and join ba ; then is abc the tri¬ 
angle required : the side ac, measured by the scale of 
equal parts will be 1.54, and the angles a and b, mea¬ 
sured by a scale of chords will be 26° 21' and 120° 18'. 

Here the arc ab cuts ac in one point only, because ab 
is greater than bc ; therefore the angle a is acute, and 

not ambiguous. 

G 


50 


PLANE TRIGONOMETRY, 


As AB, .98 


By Calculation. 


—1.99128 


Is to bc, .7912 - 
So is sine of c, 33° 21' 


1.89829 

9.74017 


To sine of a, 26° 21' 


9.63846 


9.64723 


To the angle c=33° 21' add the angle a= 26° 2T and 
the sum is 59° 42' which subtracted from 180°, leaves 
the angle b=120° 18'. 

As sine ofc, 33° 21' - - - 9.74017 


Is to sine of b, 120° 18' 
So is ab, .98 


To AC, 1.539 


9.93621 

—1.99123 


9.92744 


0.18727 


By Gunter’s Scale. 

* / 

1. Extend the compasses from .98 to .79 on the line 
of numbers, that extent will reach from 33° 2T to 26° 
21', the angle a, on the line of sines. 

2. Add the angle a= 26° 21' to the angle c=33° 2T, 
and the sum will be 59° 42'; then extend the compasses 
from 33° 21' to 59° 42', on the line of sines, that extent 
will reach from .98 to 1.54, the side ac, on the line of 
numbers. 

3. In the triangle abc, are given the angle c=r33° 21', 
the side bc=:95.12 and the side abzh60, to find the 
angles a and b, and the side ac. 








PLANK TRIGONOMETRY. 


51 


V 

By Construction , Fig. 44. 

This is constructed in the same manner as the pre¬ 
ceding example; only ab, being shorter than bc, the 
arc ab cuts ac in two points on the same side of bc ; 
hence the angle a may be either acute or obtuse. The 
side required has also two values as ac and ac. 


By Calculation. 


As ab, 60 


1.77815 


Is to bc, 95.12 

So is sine c, 33° 21' - 


1.97827 

9.74017 


11.71844 


To sine of a 


9.94029 


60° 38' acute 
119 22 obtuse 

The sum of the angles c and a subtracted from 180° 
leaves the angle b=86° T if a be acute, or 27° 17' if a be 
obtuse. 


To find the side ac answering to the acute value of 
the angle a. 

As sine of c, 33° 21' - - - - 9.74017 


Is to sine of b, 86° T - - - 9.99895 
So is ab, 60 . 1.77815 


11.77710 


To ac, 108.9 . 2.03693 

. ' , ; 

To find the side ac, answering to the obtuse value of 
the angle a. 








52 

. * / 

PLANE 

TRIGONOMETRY. 

j 


♦ 

As sine of c, 33° 

21 - - - - 

9.74017 


Is to sine of b, 27° 17' - - - 

i \ j 

So is ab, 60. 

1 * /VFr *' ** \ « . 

9.66124 

1.77815 

* • 

' / * 

To ac, 50.03 - 

i ■ ■ »y 

11.43939 

1.69922 


4. In a triangle abc, the side ab is 274, ac 306, and 
the angle b 78° 13'; required the angles a and c, and 
the side bc. 

Ans. a = 40° 33', c = 61° 14', and bc= 203.2. 

5. In a right-angled triangle, there are given the hy- 
pothenuse ac=272, and the base ab=232; to find the 
angles a and c, and the perpendicular bc. 

Ans. a=31° 28', c=58° 32'and bc=142. 

6. In a right-angled triangle abc, the hypothenuse 
ac is 150 and one side bc 69; required the angles and 
other side. 

Ans . 0=6237', a=27° 23' and ab 133.2. 

CASE 3. 

• w 

Two sides and the included angle being given, to find the 

other angles and side. 

RULE. 

Subtract the given angle from 180°, and the remain¬ 
der will be the sum of the two unknown angles. Then, 
As the sum of the two given sides, 

Is to their difference; 







PLANE TRIGONOMETRY. 


53 


So is the tangent of half the sum of the two unknown 
angles, 

To the tangent of half their difference.* * 

This half difference of the two unknown angles, add¬ 
ed to their half sums, will give the angle opposite the 


« 

* Demonstration. Let abc, Fig. 45, be the proposed triangle, 
having the two given sides ab, ac, including the given angle a. 
About a as a centre, with ac the greater of the given sides, for a dis¬ 
tance, describe a circle meeting ab produced in e and f, and bc in d ; 
join da, ec, and fc, and draw fg parallel to bc, meeting ec produced, 
in g. 

The angle eac (32.1.) is equal to the sum of the unknown angles abc, 
acb, and the angle efc at the circumference is equal to the half of 
eac at the centre (20.3. ;) therefore efc is half the sum of the un¬ 
known angles; but (32.1.) the angle abc is equal to the sum of the 
angles bad and adb or bad and acb; therefore fad is the dif¬ 
ference of the unknown angles abc, acb, and fcd, at the circum¬ 
ference is the half of that difference ; but because of the parallels 
dc, fg, the angles gfc, fcd are equal; therefore gfc is equal to half 
the difference of the unknown angles abc, acb ; but since the angle 
ecf in a semicircle, is a right angle, eg is perpendicular to cf, and 
therefore cf being radius, ec, cg are the tangents of the angles efc, 
cfg ; it is also evident that eb is the sum of the sides ba, ac, and that 
bf is the difference ; therefore since bc, fg are parallel eb : bf : : 
ec : cg (2.6.) : that is, the sum of the sides ac, ab, is to their differ¬ 
ence, as the tangent of half the sum of the angles abc, acb, is to the 
tangent of half their difference. 

To demonstrate the latter part of the rule, let ac and ab, Fig. 46, 
represent any two magnitudes whatever ; in ab produced, take bd 
equal to ad the less, and bisect ad in e. 

Then because ae is equal to ed and ac to bd, ce is equal to eb ; 
therefore ae or ed is half the sum of the given magnitudes ab, ac, and 
ce or eb is half their difference ; but ab the greater is equal to ae, eb, 
that is to half the sum added to half the difference, and ac the less, is 
equal to the excess of ae, half the sum, above ce, half the difference. 









54 PLANE TRIGONOMETRY. 

greater of the two given sides, and being subtracted 
from the half sum will give the angle opposite the less 
given side. 

After finding the angles, the other side may be found 
by Case 1. 

EXAMPLES. 


.. 1. In the triangle abc, there are given ab = 128 , ac= 
90, and the angle a=48° 12', to find the angles b and c, 
and the side bc. 

By Construction , Fig. 47. 

v • 

Draw ab=128, and make the angle a=48° 12'; 
draw ac =90, and join bc. The angle b will measure 
44° 37', the angle c 87°, IT, and the side bc 95.5. 

By Calculation . 

180° 0' 

Angle a. 4812 


ab 

ac 




128 

90 


Sum 218 Sum of the angles b and c 131 48 


Difference 38 Half sum do. 65 54 

% ♦ 

As the sum of the sides, ab, ac, 218 - - - 2.33846 

Is to their difference, 38 . 1.57978 

So is the tang, of half sum of angles b & c, 65° 54' 10.34938 

11.92916 

To tang, of half their difference, 21° 17 ' - - 9.59070 

° ,» *" v 

Half sum of the angles b and c - - 65° 54' 

Add and subtract half their difference 21 17 


Angle c.87 11 


Angle b 


. 44 37 









PLANE TRIGONOMETRY. 55 


To find the side BC. 


As sine of b 

44° 37' 

9.84656 

Is to sine of a 

48 12 

9.87243 

* 

So is ac 

90 

1.95424 

• ; v! 

• t ^ ' 

11.82667 

To BC 

95.52 

1.98011 


i i 

By Gunter's Scale. 

t , 

4 . 

Extend the compasses from 218, the sum of the sides, 
to 38, their difference, on the line of numbers, and apply 
this extent to the line of tangents from 45° to the left 
hand; then keeping the left leg of the compasses fixed, 

• I f V 

move the other leg to 65° 54' the half sum of the angles; 
that distance will reach from 45° on the same line, to 
21° 17', the half difference of the required angles. 
Whence the angles are obtained as before. 

To extend the second proportion, proceed as direct¬ 
ed in Case 1st. 

/ ' ' r ■ 1 1,1 • 

2. In a triangle abc, are given ab^109, bc=76, and 
the contained angle b= 101° 30', to find the other angles 
and side. 

( Ans. The angle a=h 30° 57', c=z47° 33', and the 
( side ac— 144.8. 

3. Given, in aright-angled triangle, the base ab=:890 
and the perpendicular bc=:787, to find the angles and 
hypothenuse. 

{Ans. the angle a=41° 29', c = 48° 31' and the 
jj hypothenuse ac = I188. 




56 PLANE TRIGONOMETRY. 

J-l , ' . , j 

CASE 4. 

,i / ' s 

Given the three sides , to find the angles. 

' i i 

* v * -. , • • • * V 

, yj 

^ RULE 1. 

Consider the longest side of the triangle as the base, 
jand on it let fall a perpendicular from the opposite 
angle. This perpendicular will divide the base into 
two parts, called segments, and the whole triangle into 
two right-angled triangles. Then, 

As the base, or sum of the segments, 

Is to the sum of the other two sides; 

So is the difference of those sides, 

To the difference of the segments of the base.* 


* Demonstration. Let abc, Fig. 48, be a triangle, and cd be 
perpendicular upon ab. About c as a centre with the less side bc 
for a radius, describe a circle, meeting ac produced, in g and e, and 
ab in f. Then it is evident that ae is equal to the sum of the sides 
ac, bc, and that ag is equal to their difference ; also because cd bi¬ 
sects fb (3.3,) it is plain that af is the difference of the segments of 
the base; but abxaf=aexag (36.3. cor. ;) therefore ab : ae : : ag : 
af (16.6 ;) that is, the base, is to the sum of the sides, as the differ¬ 
ence of the sides, is to the difference of the segments of the base. 

Cor. If af be considered the base of the triangle afc, then will cd 
be a perpendicular on the base produced ; ae will be equal to the 
sum of the sides ac, fc, and ag will be equal to their difference ; also 
ab will be equal to the sum of the segments ad, fd. But by the prece- 
ing demonstration and (16.5,) af : ae : : ag : ab ; hence when the 
perpendicular falls without the triangle, the base, is to the sum of the 
sides, as the difference of the sides, is to the sum of the segments of 
the base. 

A rule might, therefore, be given, making either side of a triangle, 
the base ; and such a rule would be rather more convenient, in some 
cases, than the one above : but then, on account of the perpendicular, 
sometimes falling within and sometimes without the triangle, it would 
require two cases, and consequently would be less simple. 





PLANE TRIGONOMETRY. 


57 


To half the base, add half the difference of the seg¬ 
ments, and the sum will be the greater segment; also 
from half the base, subtract half the difference of the 
segments, and the remainder will be the less segment. 

Then, in each of the two right-angled triangles, there 
will be known two sides, and an angle opposite to one 
of them; consequently the other angles may be found 
by Case 2. 

* , \ ' ■ ' > » 

1. In the triangle abc, are given ABr=:426, ac==365, 
and Bcr=230; required the angles. 


By Construction , Fig. 49. 


Draw ab =426; with ac— 365 in the dividers, and 
one foot in a, describe an arc, and with bc=z230, and 
one foot in b describe another arc, cutting the former in 
c; join ac, bc, and abc will be the triangle required. 
The angles measured by a scale of chords, will be a— 


32° 39', b=58° 56', and c=88° 25'. 


By Calculation 


AC 


BC 



Sum 


595 


Difference 


135 


H 


t 


58 


PLANE TRIGONOMETRY. 


As the base ab - 

426 

2.62941 

Is to the sum of the sides ac, bc - 

595 

2.77452 

So is the diff. of the sides ac, bc - 

135 

2,13033 


• 

4.90485 

* ,i 

To the din. of the segments ad, db 

188.6 

2.27544 


M'- s , ' ' } 

Half diff. of the segments 
Half base - 

- 94.3 . ; 0 

- 213. 

Segment ad - 

- 307.3 

* • 

Segment bd - 

. 

- 118.7 

As AC 

Is to AD 

So is sine of adc - 

365 

307.3 
90° ‘ 

{ 

2.56229 

2.48756 

10.00000 

x * 


■ 

12.48756 

To sine of acd 

\ 

- 57° 21' 
90 00 

9.92527 

Angle a - 

- 32 39 


As BC - 

Is to BD 

So is sine of bdc 

- 230 

- 118.7 

90° 

2.36173 

2.07445 

10.00000 


12.07445 

To sine of bcd - - 31° 4' 9.71272 

90 0 

Angle b - - - 58 56 

From 180° subtract the sum of the angles a, and b, 
91° 35', and the remainder 88° 25' is the angle c. 

















PLANE TRIGONOMETRY. 


59 


By Gunter'’s Scale. 

Extend the compasses from 426 to 595 on the line of 
numbers, that extent will reach on the same line from 
135 to 188.6 the difference of the segments of the base. 
Whence the segments of the base are found as before. 
To extend the other proportions, proceed as directed in 
Case 2. 

2. In a triangle abc, there are given ab=64, ac=t47, 
and bc — 34; required the angles. Ans. Angle a = 31° 
9', b=45° 38', and c = 103° 13'. 

3. In a triangle abc, are given Acr=88, ab=108, and 
bc=54, to find the angles. Ans. Angle a =29° 49', b 
=z54° 7', and c=96° 4'. 

RULE 2. 

Add together the arithmetical complements of the lo¬ 
garithms of the two sides containing the required angle, 
the logarithm of the half sum of the three sides, and the 
logarithm of the difference between the half sum and 
the side opposite the required angle. Then half the 
sum of these four logarithms will be the logarithmic 
cosine of half the required angle.* 


* Demonstration. Let abc, be a triangle of which the side ab, is 
greater than ac : make ad =ac, join dc, bisect it in e, and join ae ; 
draw eh parallel and equal to cb ; join jib and produce it to meet ae 
produced in g. 


Now in the triangles aed, aec, 
all the sides of the one are equal 
to the sides of the other, each to 
each; therefore (8.1) the angle 
ead=eac, and aed=aec; con¬ 
sequently aed is a right angle. 



II 







60 


PLANE TRIGONOMETRY. 


EXAMPLES. 

1. In the triangle abc, are given ab=426, ac 365, 
and bc=230 ; required the angle a. 

/ _ ' * T ' } 1 

By Calculation. 


BC 

AC 

AB 

230 

365 

426 

# 

Ar. Co. 7.43771 

Ar. Co. 7.37059 

Half sum 

2)1021 

510.5 

log. 2.70800 

Difference 

280.5 

log. 2.44793 

i 


2)19.96423 

Cos. i a. 16° 20' 

*2 

9.98211 

Angle a. 

. 32 40 




Because eh is equal and parallel to bc, bh is also equal and pa¬ 
rallel to ec (33.1); now in the triangles edf and hbf, the angle 
efd=bfii, the angle fed=fhb (29.1) and ed=ec = bh; therefore 
(26.1) ef=fh, and fd = fb. Again the angle hge = dea = a right 
angle ; if therefore with the centre f, and radius fe == fii, a circle be 
described, it will pass through the point g (31.3). 

Now 2 af=2 AD-f2 df = AD-f-AD-f-DB = ad+ab = Ac-f-AB; there¬ 
fore af = 4 ac+ b ab ; also fk == £ iK = l eh = b bc ; hence by add¬ 
ing equals to equals, af+fk = ^ ac+4 ab+^ bc, or ak = ^ (ac+ab 
+ bc) ; again ai = ak—ik = ^ (ac+ab-{-bc)—bc. 

But (Dem. to rule, case 1st.) ad : ae : : sin. aed : sin. ade : : rad. 
: cos. ead (cos. b bac). Also, ab : ag : : sin. agb : sin. abg : : rad. : 
COS. BAG (cos. 5 bac). 

Hence (c. 6.) abXad : : agxae : ; rad. : (cos. b bac) 2 . But abx 
ad = abx ac, and (cc r. 36.3) agXae = akXai = | (AC-f AC-f-Bc) x 

t 


l 









61 




PLANE TRIGONOMETRY. 

If the other angles are required, they may be found 
by Case 1. ' 

2. In a triangle abc, are given ab=.64, ac=47, and 
bc=34, to find the angle b. Ans. Angle b=45° 38'. 

3. In a triangle abc, are given ac = 88, ab=108, and 
bc=54, to find the angle c. Ans. c=96° 4'. 

The preceding rules solve all the cases of plane trian¬ 
gles, both right-angled and oblique. There are how¬ 
ever other rules, suited to right-angled triangles, which 
are sometimes more convenient than the general ones. 
Previous to giving these rules, it will be necessary to 
make the following 

Remarks on right-angled triangles. 

1. abc, Fig. 50, being a right-angled triangle, make 
one leg ab radius, that is, with the centre a, and dis¬ 
tance ab describe an arc, bf. Then it is evident that 
the other leg bc represents the tangent of the arc bf, 
or of the angle a, and the hypothenuse ac the secant 
of it. 

2. In like manner, if the leg bc, Fig. 51, be made ra¬ 
dius ; then the other leg ab will represent the tangent 
of the arc bg, or angle c, and the hypothenuse ac the 
secant of it. ■ 


(£ (ac+ab-{-bc)—bc) ; therefore abxac : £ (AC-j-AB-f bc) x (£ (ac 
-f ab+bc)—bc) : : rad. 2 : (cos. 4 bac) 2 . 

Now it is evident, that in working this proportion by logarithms, 
and taking the arithmetical complements of the logarithms of the first 
term, viz. of the two sides including the required angle, if we omit the 
logarithm of the square of radius, which is 20, it is just equivalent to 
rejecting 20 from the sum of the logarithms ; which would otherwise 
have to be done. 


I 





62 


PLANE TRIGONOMETRY. 


3. But if the hypothenuse be made radius; then each 

* « 

leg will represent the sine of its opposite angle; namely, 
the leg ab, Fig. 52, the sine of the arc ae or angle c, 
and the leg bc the sine of the arc ch, or angle a. 


The angles and one side of a right-angled triangle being given 

to find the other sides. 


RULE. 

' . m f J * 

Call any one of the sides radius, and write upon it 
the word radius; observe whether the other sides be¬ 
come sines, tangents, or secants, and write these words 
on them accordingly. Call the word written upon each 
side the name of that side. Then, 

As the name of the side given, 

Is to the name of the side required; 

So is the side given, 

To the side required.* 


Two sides of aright-angled triangle being given to find the 

angles and other side. 


RULE. 

Call either of the given sides radius, and write on 
them as before. Then, 


* Demonstration. Let aec, Fig. 53, be a right-angled triangle ; 
then it is evident that bc is the tangent, and ac the secant of the an¬ 
gle a, to the radius ab. Let ad represent the radius of the tables, 
and draw de perpendicular to ad meeting ac produced in e 5 then de 
is the tangent, and ae the secant of the angle a, to the radius ad. 
But because of the similar triangles ade, abc, ad : de : : ab : bc ; 
that is, the tabular radius : tabular tangent : : ab : bc. Also ad : 
ae : : ab : ac ; that is, the tabular radius : tabular secant: : ab : ac. 
These proportions correspond with the rule. When either of the 
other sides is made radius, the demonstration will be similar. 





PLANE TRIGONOMETRY. 


63 


As the side made radius, 

Is to the other given side; 

So is radius, 

To the name of that other side.* 

*■' V:'' ' 0 • 

After finding the angle, the other side is found as in 
the preceding rule. 

i 

EXAMPLES. 

1. In a right-angled triangle abc, are given the base 
ab~208, and the angle a =35° 16', to find the liypo- 
thenuse ac and perpendicular bc. 

By Calculation. 


The hypothenuse ac being radius. 


As the sine of c 
Is to radius 

So is AB 

, 54° 44' 

208 - 

9.91194 

10.00000 

2.31806 



12.31806 

To AC ' 

254.8 - 

2.40612 

As the sine of c, 
Is to the sine of. 
So is AB 

f \ _ 

54° 44' 

35 16 . - 

208 - 

i 

9.91194 

9.76146 

2.31806 



12.07952 

To BC, 

147.1 

2.16758 


* This is the converse of the preceding rule. 






64 


PLANE TRIGONOMETRY. 


The base ab being radius. 


As radius - 

- 

10.00000 

Is to secant of a, 35° 16' 

- 

10.08806 

So is ab, 208 


2.31806 

t 

V. 

V * I 


12.40612 

* 

To AC, 254.8 

- 

2.40612 

As radius - 

- 

10.00000 

Is to tangent of a, 35° 16' 

- 

9.84952 

So is ab, 208 

- 

2.31806 

* 


12.16758 

To bc 147.1 

- 

2.16758 

The perpendicular bc 

being 

radius. 

As tangent of c, 54° 44' 

- 

10.15048 

Is to secant of c, 54 44 - 

- 

10.23854 

So is ab, 208 

- 

2.31806 



12.55660 

To ac 254.8 

- 

2.40612 

As tangent of c, 54° 44' - 

• 

10.15048 

Is to radius, - 

- 

10.0000#* 

So is ab, 208 - 

wm 

2.31806 



12.31806 

„ i 

To Be, 147.1 


2.16758 


2. In a right-angled triangle abc, there are given the 
hypothenuse ac=272, and the base a Em 232; required 
the angles a and c, and the perpendicular bc. 










PLANE TRIGONOMETRY. 


By Calculation. 


The hypothenuse ac being radius. 


As AC • 272 
Is to ab 232 
So is radius 


2.43457 

2.36549 

10.00000 


12.36549 


To sine of c 58° 32' 
As radius 

Is to sine of a, 31° 28' 
So is ac 272 


To bc - 142 


9.93092 

10.00000 

9.71767 

2.43457 


12.15224 


2.15224 


The base ab being radius. 


As ab 232 - 2.36549 

Is to ac 272 - - - 2.43457 

So is radius - 10.00000 

12.43457 

To secant of a 31° 28' - - 10.06908 

As radius - 10.00000 

Is to tangent of a 31° 28' - 9.78675 

SoisAB 232 - - 2.36549 

12.15224 

142 - - 2.15224 


To BC 


I 










y 


66 


PLANE TRIGONOMETRY. 


3. In a right-angled triangle, are given the hypothe- 
nuse ac=36.57, and the angle a=27° 46', to find the 
base ab, and perpendicular bc. 

Ans. Base ab=32.36, and perpendicular bc=17.04. 

4. In a right-angled triangle, there are given, the 
perpendicular=193.6, and the angle opposite the base 
47° 51'; required the hypothenuse and base. 

Ans . Hypothenusc=288.5, and base=213.9 

1 / ■ V. ' 

5. Required the angles and hypothenuse of a right- 
angled triangle, the base of which is 46.72, and perpen¬ 
dicular 57.9. 

C Angle opposite the base 38° 54', angle opposite 

nSt \ the perpendicular 51° 6', and hypothenuse 74.4. 

When two sides of a right-angled triangle are given, 
the other side may be found by the following rules, 
without first finding the angles. 

1. When the hypothenuse and one leg are given, to find the 

other leg . 

RULE. 

Subtract the square of the given leg from the square 
of the hypothenuse; the square root of the remainder 
will be the leg required.* Or by logarithms thus, 

• f 

To the logarithm of the sum of the hypothenuse and 
given side, add the logarithm of their difference ; half 
this sum will be the logarithm of the leg required. 


* Demonstration. The square of the hypothenuse of a right-an¬ 
gled triangle is equal to the sum of the squares of the sides (47.1.) 
Therefore the truth of the first part of each of the rules is evident. 





PLANE TRIGONOMETRY. 


67 


2. When the two legs are given to find the hypothenuse. 

RULE. 

Add together the squares of the two given legs; the 
square root of the sum will be the hypothenuse.* Or 
by logarithms thus, 

' o r • • 

From twice the logarithm of the perpendicular, sub¬ 
tract the logarithm of the base, and add the corres¬ 
ponding natural number to the base; then, half the sum 
of the logarithms of this sum, and of the base, will be 
the logarithm of the hypothenuse. 

EXAMPLES. 

1. The hypothenuse of a right-angled triangle is 272, 
and the base 232 ; required the perpendicular. 

Calculation by Logarithms. 

Hypothenuse - - 272 

Base.232 


Sum ----- 504 log. 2.70243 

Difference - 40 1.60206 

2)4.30449 

Perpendicular - - 142 - 2.15224 


* Put A— the hypothenuse, b= the base, and p= the perpendicular, 

then (47.l)^> * 2 = A 2 —A 2 =(5.2 cor.) h+bxh—b, or p= Vh+bxh—b; 
whence from the nature of logarithms, the latter part of the first rule 
is evident. 

2 2 v 

Also (47.1) h 2 =b 2 +p 2 =bxb+L-, or A= (bxb+L -) 

which solved by logarithms will correspond with the latter part of the 
second rule. 
















68 


APPLICATION OF 


2. Given the base 186, and the perpendicular 152, 
to find the hypothenuse. 

it 

Calculation by Logarithms. 


Perpendicular 

152 log. 

i 

2.18184 

2 


Base - - - 

186 

4.36368 

2.26951 

v ( 

2.26951 


124.2 

2.09417 


/-• * # 

310.2 


log. 2.49164 

Hypothenuse 

L V 

240.2 


2)4.76115 
log. 2.38057 


3. The hypothenuse being given equal 403, and one 

leg 321 ; required the other leg. Ans. 243.7. 

4. What is the hypothenuse of aright-angled triangle, 
the base of which is 31.04, and perpendicular 27.2? 

Ans. 41.27. 

The following examples, in which trigonometry is 
applied to the mensuration of inaccessible distances 
and heights, will serve to render the student expert in 
solving the different cases, and also to elucidate its use. 

THE APPLICATION OF PLANE TRIGONOMETRY TO THE MENSU¬ 
RATION OF DISTANCES AND HEIGHTS. 

EXAMPLE 1, Fig. 54. 

Being on one side of a river and wanting to know 
the distance to a house on the other side, I measured 






I 


PLANE TRIGONOMETRY. 69 

* — r 

500 yards along the side of the river in a right line ab, 
and found the two angles* between this line and the 
object to be cab=74° 14', andcBA=49° 23'. Required 
the distance between each station and the object. 

' . -r< 

* 

Calculation. 

i ’•* ^ v. '.r f t ' • ■’•ff*' 

The sum of the angles cab and cba is 123° 37', which 
subtracted from 180° leaves the angle acb =56° 23'. 
Then by Case 1 ; 


S. ACB 

: s. cba : : 

AB 

: ac 

56° 23' 

49° 2^! 

• I'. 11 1 

500 

455.8 

S. ACB 

drllu 

& 

tU 

: s. cab : : 

AB 

: ac 

56° 23' 

74° 14' 

500 

577.8 

EXAMPLE 2, Fig. 

55. 



Suppose I want to know the distance between two 
places a and b, accessible at both ends of the line ab, 
and that I measured ac=735 yards, and bc=840 ; also 
the angle acb = 55° 40'. What is the distance between 
a and b ? 


Calculation. 

The angle acb=55° 40', being subtracted from 180°, 
leaves 124° 20' ; the half of which is 62° 10 '. Then by 
Case 3. 


* The angles may be taken with a common surveyor’s compass ; 
or more accurately with an instrument called a theodolite. 



70 


APPLICATION OP 


CAB-fCBA , . CAB- 

BC-f ac : bc—ac : : tangent .— - : tangent -— 


—cba 




1575 


105 


62° 10' 


7° 12' 

CAB-CBA 


To and from C -.i + -— =62° 10', add and sub. 

2 2 

= 7° 12', and we shall have cab=69° 22', and cba=54° 58'. 

Then, 

i s. abc : s. ace : ^ ac : ab 
54° 58' 55° 40' 735 741 


EXAMPLE 3, Fig 56. 

f . *T , 

Wanting to know the distance between two inacces¬ 
sible objects a and b, I measured a base line cd=300 
yards: at c the angle bcd was 58° 20' and acd 95° 20'; 
at d the angle cda was 53° 30' and cdb 98° 45'. Re¬ 
quired the distance ab. 


Calculation. 

' . • • i 

1. In the triangle acd, are given the angles acd=95° 
20', adc=53° 30', and the side cd=300, to find ac= 
465.98. 

2. In the triangle bcd, are given the angle bcd= 
58° 20', bdc=98° 45', and side cd=300, to find bc= 

761.47. 

3. In the triangle acb we have now given the angle 
acb=acd — bcd==:37 0 , the side ac=465.98 and bc= 

761.47, to find ab=479.8 yards, the distance required. 

EXAMPLE 4, Fig. 57. 

Being on one side of a river and observing three ob¬ 
jects, a b and c stand on the other side, whose distances 






PLANE TRIGONOMETRY. 


71 


I 


apart I knew to be, ab=3 miles, ac=2, and bc= 
1.8, I took a station d, in a straight line with the objects 
a and c, being nearer the former, and found the angle 
adb=17° 47'. Required my distance from each of the 
objects. 

S'* y ^ 

Construction. 

* \ ^ • *■ / - ( 9 ’ * 

\ * ' 

With the three given distances, describe the triangle 
abc ; from b, draw be parallel to ca, and draw bd mak¬ 
ing the angle ebd=17° 47' (the given angle adb) and 
meeting ca produced, in d : then ad, cd and bd will be 
the distance required.* 

Calculation . 

1. In the triangle abc we have all the sides given, to 
find the angle c=104° 8'. 

2. Subtract the sum of the angles d and c from 180°, 
the remainder 58° 5' will be the angle dbc ; then in the 
triangle bcd we know all the angles and the side bc to 
find dc =5.003 and bd=5.715; therefore da= dc — ac 
= 3.003. 

# 

example 5, Fig. 58. 

From a station at d, I perceived three objects, a, b 
and c, whose distances from each other I knew to be as 
follow: ab=12 miles, bc=7.2 miles, and ac=8 miles; 
at d, I took the angle cdb=25° and adc=19°. Hence 
it is required to find my distance from each of the ob¬ 
jects. 


* Demonstration. By construction, the distances ab, bc and ac 
are equal to the given distances ; also the angle (29.1) bdc~ the angle 
pbe — the given angle. 









72 APPLICATION OF 

Construction. 

With the given distances describe the triangle abc ; 
at b, make the angle eba— 19°=the given angle adc, 
and at a, make the angle EAB=25°=the given angle 
bdc; draw ae, and be meeting in e, and (by prob. 10.) 
describe a circle that shall pass through the points a, 
e and b: join ce and produce it to meet the circle in 
d, and join ad, bd, then will ad, cd and bd be the dis¬ 
tances required.* 

f S f 

Calculation. 

1. In the triangle abc, all the sides are given, to find 
the angle bac=35° 35'. 

2. In the triangle aeb are given all the angles, viz. 
eab=25°, eba=19° and aeb=136°, and the side ab= 
12, to find ae=5.624. 


* Demonstration. The angle adc standing on the same arc with 
the angle abe is equal to it (21.3.) For the same reason the angle 
bdc is equal to the angle bae ; but by construction the angles abe and 
bae are equal to the given angles ; therefore the angles adc and bdc 
are equal to the given angles. 

Note .—When the given angles adc, bdc arc respectively equal to 
the angles abc, bac, the point e will fall on the point c, the circle will 
pass through the points a, c, and e, and the point d may be any where 
in the arc adb ; consequently, in this case, the situation of the point 
d, or its distance from each of the objects a, b, c, cannot be deter¬ 
mined from the data given. 

It may not be improper also to observe, that even when the angle 
adb, which is the sum of the given angles, is equal to the sum of the 
angles abc, bac, or which is the same thing, is the supplement of the 
angle acb, the circle passes through the points a, c, b ; but then the 
angles adc, bdc, unless they have been erroneously taken, will be re¬ 
spectively equal to the angles abc, bac. 





PLANE TRIGONOMETRY. 


73 


3. In the triangle cae we have given the side ac=8, 
ae— 5.624, and the angle cae=bac—eab=10° 35', to 
find the angle ace =22° 41'. 

4. In the triangle dac, all the angles are given, viz. 
adc =19°, acd=22° 41' and cad =180°—the sum of 
the angles adc and acd,= 138° 19', and the side ac=8, 
to find ad =9.47 miles and cd= 16.34. 

In the triangle abd, we have the angle adb=adc-(- 
bdc=44°, the angle bad = cad—bac=102° 44', and the 
side ab=12, to find bd= 16.85 miles. 

* i 

' / . v * • 

example 6. Fig. 59. 

A person having a triangular field, the sides of which 
measure ab=50 perches, ac=46 perches, and bc=40 
perches, wishes to have a w T ell dug in it, that shall be 
equally distant from the corners a, b, and c. What must 
be its distance from each corner, and by what angle 
from the corner a, may its place be found ? 

Construction. 

With the given sides construct the triangle abc, and 
(by Prob. 10.) describe a circle that shall pass through 
the points a, b, and c ; then the centre e of this circle is 
the required place of the well.* 

Calculation. 

1. In the triangle abc, all the sides are given, to find 
the angle abc =60° 16'. 

2. Join ce and produce it to meet the circumference 
in d ; also join ae and ad ; then the* angles adc, abc 


K 


* The demonstration of this is plain (1.3. cor.) 




74 


f 


APPLICATION OF 


being angles in the same segment are equal, also the 
angle dac being an angle in a semicircle, is a right an¬ 
gle : therefore in the right-angled triangle dac, we have 
the angle adc=abc=60° 16', and the side ac, to find 
cd==52.98 perches. The half of cd is =26.49 perches 
=cE=the distance of the well from each corner. 

' **• . ' 4 

3. The angle acd=90° — adc=29° 44'; but because 
aec is an isosceles triangle, the angle cae=ace=29° 
44' the angle required. 

example 7. Fig. 61. 

< - v . i 

Wishing to know the height of a steeple situated on 
a horizontal plane, I measured 100 feet in a right line 
from its base, and then took the angle of elevation* of 
the top, which I found to be 47° 30', the centre of the 
quadrant being 5 feet above the ground: required the 
height of the steeple. 


* Angles of elevation, or of depression, are usually taken with an 
instrument called a quadrant, the arc of which is divided into 90 
equal parts or degrees, and those when the instrument is sufficiently 
large may be subdivided into halves, quarters, &c. From the centre 
a plummet is suspended by a fine silk thread. Fig. 60 is a represen¬ 
tation of this instrument. 

To take an angle of elevation, hold the quadrant in a vertical position, 
and, the degrees being numbered from b towards c, with the eye at c, 
look along the side ca, moving the quadrant till the top of the object is 
seen in a range with this side ; then the angle bad made by the plummet 
with the side ba, will be the angle of elevation required. 

Angles of depression are taken in the same manner, except that then 
the eye is applied to the centre of the quadrant. 

Note. —In finding the height of an object, it is best to take such a 
position that the observed angle of altitude may be about 45° ; for 
when the observed angle is 45°, a small error committed in taking it, 
makes the least error in the computed height of the object. 


l 


i 



PLANE TRIGONOMETRY. 


/5 


» 

. Calculation. 

* t i 

In the right-angled triangle dec, we have the angle 
cde=47° 30', and the base de=ab=100 feet to find 
ce=109.13 feet; to ce add eb=da=5 feet the height 
of the quadrant, and it will give bc=114.13 feet, the re¬ 
quired height of the steeple. 

example 8. Fig. 62. 

Wishing to know the height of a tree situated in a 
bog, at a station d which appeared to be on a level 
with the bottom of the tree, I took the angle of eleva¬ 
tion bdc=51° 30'; I then measured da=75 feet in a 

y 

direct line from the tree, and at a, took the angle of 
elevation bac=26° 30'. Required the height of the 
tree. 

i ✓ 

Calculation. 

1. Because the exterior angle of a triangle is equal to 
the sum of the two interior and opposite ones, the an¬ 
gle bdc=dac-(-acd ; therefore acd=bdc —dac=25° : 
now in the triangle adc we have dac=26 0 30', acd=25°, 
and ad=75, to find dc=79.18. 

2. In the right-angled triangle dbc are given dc = 
79.18, and the angle bdc=51° 30' to find bc= 61.97 
feet, the required height of the tree. 

example 9. Fig. 63. 

> v • • 

Wanting to know the height of a tower ec, which 
stood upon a hill, at a, 1 took the angle of elevation 
c A b= 44°; I then measured ad 134 yards, on level 
ground, in a straight line towards the tower; at d the 
angle cdb was 67* 50' and edb 51°. Required the 
height of the tower and also of the hill. 



76 


APPLICATION OF 


Calculation . 

* k • i 

V i ' . , *• ' ' \ ? 

* . » , I * I r 

1. In the triangle adc, we have the angle dac=44°, 
the angle acd=bdc —dac=23° 50', and the side ad, to 
find dc= 230.4. 

, r 

‘ 

2. In the triangle dec all the angles are given, viz. 
cde =bdc— bde=16° 50', dce=90°— bdc=22° 10', dec 
= 180°—the sum of the angles cde and dce,= 141°, 
and cd= 230.4, to find ce= 106 yards, the height of the 
tower. 

Y A 

3. In the right-angled triangle dbc, we have the an¬ 
gle bdc= 67° 50', and the side dc =230.4, to find bc = 
213.4; then be=bc—ce=213.4 — 106=107.4 yards, 
the height of the hill. 

: ■ ' J 

EXAMPLE 10. Fig 64. 

An obelisk ad standing on the top of a declivity, I 
measured from its bottom a distance ab =40 feet, and 
then took the angle abd=41° ; going on in the same di¬ 
rection 60 feet farther to c, I took the angle acd=23° 
45' : what was the height of the obelisk ? 


Calculation. 

1. In the triangle bcd, we have given the angle bcd, 
= 23° 45', the angle bdc= abd — bcd = 17° 15', and side 
bc= 60, to find bd= 81.49. 

2. In the triangle abd are given the side ab=40, bd 
=81.49, and the angle abd=41°, to find ad= 57.63 
feet, the height of the obelisk. 


PLANE TRIGONOMETRY. 


77 


EXAMPLE 11. Fig. 65. 

Wanting to know the height of an object on the 
other side of a river, but which appeared to be on a 
level with the place where I stood, close by the side of 
the river; and not having room to go backward on the 
same plane, on account of the immediate rise of the 
bank, I placed a mark where I stood, and measured in 
a direct line from the object, up the hill, whose ascent 
was so regular that I might account it a right line, to 
the distance of 132 yards, where I perceived that I was 
above the level of the top of the object; I there 
took the angle of depression of the mark by the river’s 
side equal 42°, of the bottom of the object equal 27°, 
and of its top equal 19° : required the height of the 
object. 

Calculation . 

1. In the triangle acd, are given the angle cad=eda 
=27°, acd =180°—cde (fcd)=138° and the side cd= 
132, to find ad= 194.55 yards. 

2. In the triangle abd, we have given adb=ade —bde 
=8°, abd=bed-}-bde=109 o and ad =194.55, to find ab 
=28.64 yards, the required height of the object. 


example 12. Fig. 66. 

A May-pole whose height was 100 feet, standing on 
a horizontal plane, was broken by a blast of wind, and 
the extremity of the top part struck the ground at the 
distance of 34 feet from the bottom of the pole: re¬ 
quired the length of each part. 





78 APPLICATION OF 

Construction. 

/ \[ . K 

Draw ab=34, and perpendicular to it, make bc= 
100; join ac and bisect it in d, and draw de perpendi¬ 
cular to ac, meeting bc in e ; then AE=cE=the part bro¬ 
ken off.* 

Calculation. 

• i * _ , ^ * | 

1. In the right-angled triangle abc, we have ab = 34 
and bc= 100, to find the angle c= 18° 47'. 

2. In the right-angled triangle abe, we have aeb= 
ace-}-cae=2 ace=37° 34', and ab=34, to find ae = 
55.77 feet, one of the parts ; and 100 — 55.77 =44.23 
feet, the other part. 

*> » 

PRACTICAL QUESTIONS. 

1. At 85 feet distance from the bottom of a tower, 

the angle of its elevation was found to be 52° 30': re¬ 
quired the altitude of the tower. Jins. 110.8 feet. 

2. To find the distance of an inaccessible object, I 
measured a line of 73 yards, and at each end of it took 


* Demonstration. In the triangles aed, dec, the angle ade=cde, 
the side ad=cd, and de is common to the two triangles, therefore 
(4.1) AE = CE. 


Note .—This question may be neatly solved in the following man¬ 
ner without finding either of the angles. Thus, draw df perpen¬ 
dicular to bc, then (31.3 and cor. 8.6) fc : dc : : dc : ce ; conse- 

, and fc^^ec; there- 


quently ce 


dc 2 , o ac 2 ab 2 + bc 2 
: — ; but dc 2 = 


fore ce 


fc 4 

_ab 2 -1-bc 2 34- 2 -|-100 


1156+10000 11156 


2ec 200 

the same as before nearly. 


200 


200 


55.78, 













PLANE TRIGONOMETRY. 79 

the angle of position of the object and the other end, 
and found the one to be 90°, and the other 61° 45': re¬ 
quired the distance of the object from each station. 

Am. 135.9 yards from one, and 154.2 from the other. 

* •: ( ; 

3. Wishing to know the distance between two trees 

c and d, standing in a bog, I measured a base line ab= 
339 feet; at a the angle bad was 100° and bac 36° 30'; 
at b the angle abc was 121° and abd 49°: required the 
distance between the trees. Ans. 697| feet. 

4. Observing three steeples, a, b and c, in a town at a 
distance, whose distances asunder are known to be as 
follows, viz. ab=213, ac=404, and bc=262 yards, I 
took their angles of position from the place d where I 
stood, which was nearest the steeple b, and found the 
angle adb=13° 30'; and the angle bdc=:29 0 50'. Re¬ 
quired my distance from each of the three steeples. 
Am . ad^=571 yards, bd=389 yards, and cd=514 yards. 

5. A May-pole, whose top was broken off by a blast 

of wind, struck the ground at 15 feet distance from the 
foot of the pole: what was the height of the whole May- 
pole, supposing the length of the broken piece to be 39 
feet? Ans 75 feet. 

6. At a certain place the angle of elevation of an in¬ 
accessible tower was 26° 30'; but measuring 75 feet in 
a direct line towards it, the angle was then found to be 
51° 30': required the height of the tower and its distance 
from the last station. Ans . Height 62 feet, distance 
49. 

7. From the top of a tower by the sea side, of 143 
feet high, l observed that the angle of depression of a 


80 


APPLICATION OF, &C. 


ship’s bottom, then at anchor, was 35°; what was its 
distance from the bottom of the wall ? Jins. 204.2 feet. 

8. There are two columns left standing upright in 
the ruins of Persepolis; the one is 64 feet above the 
plane, and the other 50; in a right line between these 
stands an ancient statue, the head of which is 97 feet 
from the summit of the higher, and 86 from that of the 
lower column; and the distance between the lower 
column and the centre of the statue’s base is 76 feet: 
required the distance between the top of the columns. 

A ns. 157 feet. 


SURVEYING. 



CHAPTER I 

ON THE DIMENSIONS OF A SURVEY. 

1. Surveying is the art of measuring, laying out and 
dividing land. 

2. A Four-Pole Cham is an instrument used for mea¬ 
suring the boundaries of a survey. It is, as its name 
imports, 4 poles or 66 feet in length, and is divided into 
100 equal parts or links. The length of a link is there¬ 
fore 7.92 inches. •> 

Note .—A Four-Pole Chain is frequently called sim¬ 
ply a chain. 

3. A Two-Pole Chain is 2 poles or 33 feet in length, 
and is usually divided into 50 equal parts or links. 
When it is thus divided, the links are of the same length 
as in a four-pole chain ; and the measures taken with 
it are reduced to four-pole chains previous to using 
them in calculation. 

• • > f 

Sometimes the two-pole chain is divided into 40 links. 
in which case, each two links is the one-tenth of a 
perch. Measures taken with a two-pole chain, thus di¬ 
vided, are usually expressed in perches and tenths. 

L 


t 






*1 ■ 




\ 

82 DIMENSIONS OF A SURVEY. CHAP. I. 

4. The Distance of a line in surveying, is its length, 
estimated in a horizontal direction. It is generally ex¬ 
pressed either in chains and links, or in perches and 
tenths. 

. 

5. A Meridian or Meridian Line , is any line that runs 
due north or south. 

JVote. —All the meridians passing through any sur¬ 
vey of moderate extent may be considered as straight 
lines, parallel to one another.* 

i * , 

6. The Bearing or Coarse of a line, is the angle which 
it makes, with a meridian passing through one end; and 
is reckoned from the North or South Points of the hori¬ 
zon towards the East or West Points. 

Thus, supposing the line ns, Fig. 77, to be a meri¬ 
dian, and the angle sab to be 50°; then the bearing of 
ab from the point a, is 50° to the east of south; which 
is usually expressed thus: S. 50° E., and read, south, 
fifty degrees east. 

7. The Reverse Bearing of a line is the bearing taken 
from the other end of the line. 

Note. —The bearing and the reverse bearing of a line, 
arc angles of the same magnitude,f but lying between 


* The meridians are in reality curve lines which meet in the north 
and south poles of the earth. No two of them are therefore exactly 
parallel; but in usual surveys their deviation from parallelism is so 
very small, that there is no sensible error in considering them so. 

t As the meridians are not exactly parallel, this is not strictly true, 
except in a few cases ; but the difference is too small to be observed 


/ 




CHAP. I. 


DIMENSIONS OF A SURVEY. 


83 


directly opposite points. Tims, if the bearing of ab, 
from the end a, is S. 50° E., the bearing of the same 
line from the end b, is N. 50° W. 

8. A Circumferentor or Surveyor's Compass , is an in¬ 
strument used to take the bearings of lines. 

The circumference of its face is divided into degrees, 
and in some of the larger ones into half degrees, in such 
manner that two opposite points may be exactly in the 
direction of the sights with which the instrument is fur¬ 
nished. These points are the north and south points 
of the instrument. Midway between them, on the cir¬ 
cumference, are the east and west points. The degrees 
are numbered from 0° to 90°, each way from the north 
and south points to the east and west ones. In the 
centre of the face is a pin, finely pointed, which sup¬ 
ports a Magnetic Needle, moving freely within the in¬ 
strument. The instrument, when used, is placed on a 
staff, having a pointed iron at the bottom, and a ball 
and socket at the top. 

The Chain and Compass are the instruments with 
which the dimensions of surveys in this country are gen¬ 
erally taken. It is important to have them accurately 
made. In the selection of a compass, particular atten¬ 
tion should be directed to the settling of the needle. 
If, when the needle has been moved out of its natural 
position, it settles very soon, it is defective; either its 
magnetic virtue is weak, or it does not move with suffi¬ 
cient freedom on the pin. 

9. The Difference of Latitude , or the JYorthing or 


in practice. In the latitude of Philadelphia the greatest difference be¬ 
tween the bearing and reverse bearing of a line, a rnile in length, is 
only 44". In higher latitudes the difference is greater. 








84 


DIMENSIONS OF A SURVEY. 


CHAP. U 


Southing of a line, is the distance that one end is further 
north or south than the other end; or it is the distance 
which is intercepted on a meridian passing through one 
end, between this end and a perpendicular to the meri¬ 
dian, from the other end. 

Thus, if ns, Fig. 77, be a meridian passing through 
the end a, of the line ab, and b6 be perpendicular to ns, 
then is pJb the difference of latitude or southing of ab. 

10. The Departure or the Easting or Westing of a line 
is the distance that one end is further east or west than 
the other end; or it is the distance from one end, per¬ 
pendicular to a meridian passing through the other end. 

Thus b6, Fig. 77, is the departure or easting of the 
line ab. 

But if ns be a meridian, and ac perpendicular to it, 

* • 

and if the bearing of the line be taken from b to a, 
then is bc the difference of latitude or northing, and ac 
the departure or westing, of the line ab. 

Note. —It is evident from the definitions that the Dis¬ 
tance, Difference of Latitude and the Departure, form 
the sides of a right-angled triangle; in which, consider¬ 
ing the departure as the base, the perpendicular is the 
difference of latitude, the hypothenuse is the distance, 
and the angle at the perpendicular is the bearing. 

11. The Meridian Distance of any station, is its dis¬ 
tance from a meridian passing through the first station 
of the survey, or any other assumed point. v 

12. The Traverse Table is a table containing the dif- 



CHAP. I. DIMENSIONS OF A SURVEY. 85 

ferences of latitude and the departures, computed to 
different courses and distances. 

\ \ . • V > 

’ J - • . 

13. The Area or Content of a tract of land is the hori¬ 
zontal surface included within its boundaries, expressed 
in known measures, as Acres, Roods, and Perches. 

14. In going round a tract of land and returning to 
the place of beginning, it is evident that the whole 
northing which has been made, must be equal to the 
southing, and the easting to the westing; or in other 
words, that the sum of all the northings must be equal 
to that of the southings, and that of the eastings to that 
of the westings. 

This principle enables us to judge of the accuracy 
of a survey, when the bearings and distances of all the 
sides have been taken. If the sums of the computed 
northings and southings are equal, and also those of 
the eastings and westings; or, if, though not exactly 
equal, they are very nearly so, we may conclude that 
the survey has been correctly made; as very small dif¬ 
ferences in these sums may be imputed to little, una¬ 
voidable errors in taking the bearings and measuring 
the distances. But when the sum of the northings dif¬ 
fers considerably from that of the southings, or that of 
the eastings from that of the westings, we must infer 
that an error has been made, too great to be admitted. 
In this case a re-survey should be taken. 

It is a rule with some of our best practical surveyors, 
that when the difference between the sums of the north¬ 
ings and southings, called the error in latitude , or that be¬ 
tween the sums of the eastings and westings, called the 
error in departure , exceeds one link for every five chains 
in the sum of the distances, a re-survey ought to be 
made. 


i 


86 DIMENSIONS OF A SURVEY. CHAP. I. 

/ * < 

When the errors in latitude and departure fall within 
the limits just mentioned, they should be properly ap¬ 
portioned among the several latitudes* and departures; 
we shall thus obtain what are called the corrected la¬ 
titudes and departures. The method of doing this will 
be given in one of the following problems. 

« f \v f . , J \ 

. • f t ' ‘ J 

• . 

PROBLEM I./ -flier 

To reduce Iwo-polc chains and links to Jour-pole chains and 

links. 

it 

• '* * ■ , i • ^ 

RULE. 

J. If the number of chains is even, divide it by 2, and 
to the quotient annex the given number of links. 

s - * ‘ * 

2. If the number of chains is odd, divide by 2 as be¬ 
fore, for the chains; and for the 1 that is off, add 50 to 
the given number of links. 

EXAMPLES. 

1. In 16 two-pole chains and 37 links, how many lour- 
pole chains and links ? Ans. 8 ch. 37 links, or 8.37 ch. 

2. How many four-pole chains and links are there in 
17 two-pole chains and 42 links ? Ans. 8.92 ch. 

3. How many four-pole chains and links are there in 
22 two-pole chains and 7 links? Ans. 11.07 ch. 


* In order to conciseness of expression, difference of latitude is fre¬ 
quently called simply, latitude. 




CHAP. I. 


r 

DIMENSIONS OF A SURVEY. 

. • * 
A V v * ; 

PROBLEM II. 


1)7 


I ' 


To reduce tivo-pole chains and links to perches and hundredths 

of a perch. 


’ RULE. 

Multiply the links by 4, for the hundredths, and the 
chains by 2, for the perches. If the hundredths exceed 
100, set down the excess and add 1 to the perches. 

• vi ■ ,, -* " h\ 

JVote .— This rule supposes the two-pole chain to be 
divided into 50 links. 

• # 

• m 1 ‘ ^ *. 4 .It I 

N 

.. 

EXAMPLES. 

r 

1. Reduce 17 two-pole chains and 21 links to perches 
and hundredths. Ans. 34.84 per. 

2. Reduce 15 two-pole chains and 38 links to perches 
and hundredths. Ans. 31.52 per. 


3. Reduce 57 two-pole chains and 49 links to perches 
and hundredths. Ans. 115.96 per. 


PROBLEM III. 

* i 

To reduce square four-pole chains to acres. 

• RULE. 

* 

Divide by 10, and the quotient will be the acres. If 
there is a decimal in the quotient, multiply it by 4, for 
the roods; and the decimal of these by 40, for the 
perches. 


88 DIMENSIONS OF A SURVEY. CHAP. I. 

• « r ; • \, ' ; ’ jJL a., i 

EXAMPLES. 

1. Reduce 523.2791 square chains to acres. 

{ ’ ’ . , 10)523.2791 

_ 

52.32791 


/ 1.31164 
40 

• - 

12.46560 

./ins. 52 ac. 1 r. 12 p. 

• u %■ ’ i ' 

• . ■ v , < 'i. w j ..... a; y •. 

2. Reduce 41.9682 square chains to acres. 

** < ‘ Ans. 4 ac. 0 r. 31 p. 

.i , * . .. \ 

3. Reduce 132.925 square chains to acres. 

Ans. 13 ac. 1 r. 6.8 p. 

PROBLEM IV. 

To reduce acres , roods and perches to square chains. 

RULE. 

Divide the perches by 40 and prefix the roods; di¬ 
vide the result by 4 and prefix the acres; then this lat¬ 
ter result, multiplied by 10, will give the square chains. 

Or reduce the given quantity to perches and divide 
by 16. 

EXAMPLES. 

. t • 

1. Reduce 13 ac. 1 r. 10 jt. to square chains. 

40)10 

\ _ • ■ \ / i 

4)1.25 


13.3125 J= 133.125 stj. ch. 







CHAP. I. 


DIMENSIONS OF A SURVEY. 


89 


2. Reduce 127 etc. 3 r. 33 p. to square chains. 

Ans. 1278.9375 sq. ch. 

3. Reduce 35 ac. 0 r. 20 p. to square chains. 

Ans. 351.25 sq. ch. 

PROBLEM V. 

To find the hearing of a line. 

1. Let a stake of six or eight feet in length be set up 
perpendicularly at the far end of the line. Set up the 
compass staff perpendicularly at the beginning of the 
line, and placing the compass on the staff, adjust it to 
a horizontal position; the ball and socket admitting a 
motion for that purpose. This position can be de¬ 
termined with sufficient accuracy, by observing whe¬ 
ther, when the compass is turned round, the ends of 
the needle remain at the same height above the face of 
the instrument. 

2. Turn the compass round so as to bring the south 
end of it towards the stake at the far end of the line. 
Then applying the eye to the sight at the north 
end, move the compass gently round till the stake can 
be seen through the fine slits in both sights, and let it 
remain in this position. 

3. When the needle has settled, observe the number 
of degrees and parts of a degree, that are intercepted 
between the south end of the needle and the north or 
south point of the compass, to whichever it is nearest; 
which will be the bearing, reckoning it from that point, 
towards the east if the south end of the needle is to the 
right hand, but towards the west if it is to the left hand. 

_ * 

JYote 1.—The bearing thus obtained may be,, and 

should be, verified by going to the far end of the line. 

M 


90 


DIMENSIONS OF A SURVEY. 


CHAP. I. 


and from thence taking the bearing to the first end; 
which, if both bearings are correct, will be the reverse 
of the former. 

Note 2.—When there is a fence on the side, or other 
obstacle in the way, preventing the stake at one end 
from being seen through the compass sights at the 
other end, the bearing may be obtained by setting up 
the compass and stake at small equal distances to the 
right or left, so that the line joining them may be pa¬ 
rallel to the side. 

Note 3.—The method of obtaining the bearing be¬ 
tween two stations when there are obstacles in the way, 
which also prevent a parallel bearing being readily ta¬ 
ken, or when the stations are too distant to be seen 
from each other, will be noticed in the next chapter. 

PROBLEM VI. 

To measure the distance of a line. 

For convenience in marking the termination of the 
chain in measuring, ten iron pins should be provided, 
about a foot in length and terminated at top by a small 
ring, to which a piece of red flannel or other conspicu¬ 
ous substance should be tied, in order that the pins may 
be readily found, when set up among high grass or in 
other situations where they would not otherwise be 
easily discovered. 

Let the person who is to go foremost in carrying 
the chain, take nine of the pins in his left hand, and one 
end of the chain and the other pin in his right hand ; 
then he moving on in the direction of the line, let an¬ 
other person take the other end of the chain and hold 
it at the beginning of the line. When the leader has 
moved on till the chain is stretched tight, he must set 


CHAP. I. 


DIMENSIONS OP A SURVEY. 


91 


down the pin, perpendicularly, exactly at the end of 
the chain, the hinder chain-man taking care, that the 
chain is in the direction of the line, which is readily 
determined by observing whether it is in a range with a 
stake previously set up at the far end of the line. When 
the leader has not his end of the chain in the direction 

of the line, the hinder chain-man can direct him which 

£ / 

way to move, by a motion of his left hand. When the 
distance of one chain or half chain* has been thus de¬ 
termined, the carriers, taking hold of the two ends of 
the chain, move on till the hinder one comes to the pin 
which was set up by the other; then the chain being 
stretched, the person at the fore end of it sets up ano¬ 
ther pin as before; the hinder chain-man then taking 
up the pin at his end, they proceed to a third distance 
of the chain ; and so on. When the person at the fore 
end of the chain has set up all his pins, he still moves 
on another length of the chain, and then setting his 
foot on it to keep it in place, he cries “ out” The hin¬ 
der chain man then comes forward, and counts to him 
the ten pins ; and he setting up one of them at the end of 
the chain, again moves on, dragging the chain after 
him, till he is checked by the hinder chain-man, who 
getting the hind end of the chain applies it as before to 
the pin set up. The number of outs should be careful¬ 
ly noticed; each out being ten chains, when a four-pole 
chain is used, but only five when the measuring is done 
with a two-pole chain. When arrived at the end of 
the line, the number of pins which the one at the fore 
end of the chain has set up since the last out , and the 
number of links from the last pin to the end of the line, 
must be carefully noted. From these, and the number 
of outs, the distance measured is readily determined. 

* When a two-pole chain is used, one length of it may properly be 
called a half chain. 




92 


DIMENSIONS OF A SURVEY. 


CHAP. I. 


All slant or inclined surfaces, as the sides of a hill, 
should be measured horizontally, and not on the plane 
or surface of the hill. To effect this, the hind end of 
the chain, in ascending a hill, should be raised from the 
ground till it is on a level with the fore end, and, by 
means of a plummet and line, or when the hill is not 
very steep, by estimation, should be held perpendicular¬ 
ly above the termination of the preceding chain. In 
descending a hill, the fore end of the chain should be 
raised in the same manner, and the plummet being 
suspended from it will show the commencement of the 
succeeding chain. 

% 

PROBLEM VII. 

X C 

To protract a Survey , having the hearings and distances of 

the sides given . 

• 

The method of doing this will be best understood 
by an example. Thus, 

Suppose the following field-notes to be given, it is re¬ 
quired to protract the survey. 






Ch. 

L 

N. 

50° 

E. 

9.00 

o 

Axd * 

S. 

32° 

E. 

16.38 

3. 

S. 

41° 

W. 

6.30 

4. 


West 

8.43 

5. 

N. 

79° 

W. 

10.92 

0. 

N. 

5° 

E. 

11.25 

7. 

S. 

83° 

E. 

6.48 


Method 1st. 

Draw ns, Fig. 75, to represent a meridian line; then 
n standing for the north and s for the south, the east 
will be to the right hand and the west to the left. In 



CHAP. I. DIMENSIONS OF A SURVEY. 93 

ns take any convenient point as a for the place of be¬ 
ginning, and apply the straight edge of the protractor 
to the line, with the centre to the point a, and the arch 
turned towards the east, because the first bearing is 
easterly; then holding the protractor in this position, 
prick off 50° the first bearing, from the north end, be¬ 
cause the bearing is from the north; through this 
point and the point a, draw the line ab on which lay 
9.60 chains, the first distance from a to b. Now 
apply the centre of the protractor to the point b, with 
the arch turned toward the east, because the second 
bearing is easterly, and move it till the line ab pro¬ 
duced cuts the first bearing 50°; the straight edge of 
the protractor will then be parallel to the meridian ns ; 
hold it in this position, and from the south end prick 
off the second bearing 32°; draw bc and on it lay the 
second distance 16.38 chains. Proceed in the same 
manner at each station, observing always, previous to 
pricking off the succeeding bearing, to have the arch 
of the protractor turned easterly or westerly according 
to that bearing, and to have its straight edge parallel 
to the meridian; this last may always be done by ap¬ 
plying the centre to the station point, and making the 
preceding distance line produced if necessary, cut the 
degrees of the preceding bearing: It may also be 
done by drawing a straight line through each station, 
parallel to the first meridian. 

When the survey is correct and the protraction accu¬ 
rately performed, the end of the last distance will fall 
on the place of beginning. 

Method 2nd. 

With the chord of 60° describe the circle nesw, Fig. 
7(3j|nd draw the diameter ns. Take the several bear- 


94 


CHAP. I* 


DIMENSIONS OF A SURVEY. 


ings from the line of chords, and lay them off on the 
circumference from n or s according as the bearing is 
northerly or southerly, and towards e or w according as 
it is easterly or westerly, and number them 1, 2, 3,4, &c. 
as in the figure. From a the centre of the circle, to 1 
draw a 1 , on which lay the first distance from a to b ; 
parallel to a 2 draw bc on which lay the second dis¬ 
tance from b to c : parallel to a 3 draw cd on which lay 
the third distance from c to d; proceed in the same 
manner with the other bearings and distances. 


example 2. 


The following field-notes are given, to protract the 
survey. 


Ch. 


1. N. 15° 00' E. 20 

2. N. 37° 30' E. 10 

3. East 7.50 

4. S. 11° 00' E. 12.50 

5. South 13.50 

6. West 10. 

7. S. 36° 30' W. 10. - 

8. N. 38° 15' W. 8.50 


PROBLEM VIII. 

The bearing of two lines from the same station being given, 
to find the angle contained between them. 

rule. 

When they run from the same point of the compass, 
towards the same point, subtract the less from the 
greater. 


When they run from the same 
points, add them together. 


point, towards diff^mt 




CHAP. I. 


DIMENSIONS OF A SURVEY. 


95 


When they run from different points, towards the 
same point, add them together, and take the supplement 
of the sum. 

When they run from different points, towards different 
points, subtract the less from the greater, and take the 
supplement of the remainder. 

Note. —When the'bearing of one of the lines is given 
towards the station, instead of from it, take the reverse 
bearing of such line ; the angle may then be found by 
the above rule. 


EXAMPLES. 

1. Given the bearing of the line ab, Fig. 67, r®3i° 
E., and ad, N. 58° E.; required the angle a. 

ad, N. 58° E. 

• ab, N. 34° E. 


Angle Am24 

2. Given the bearing of ba, Fig. 67, S. 34° W., and 
bc, S. 35° E.; required the angle b. Ans. b==69°. 

3. Given the bearing of bc, Fig. 67, S. 35° E., and cd, 
S. 87° W.; required the angle c. Ans. 58°. 

4. Given the bearing of dc, Fig. 67, N. 87° E., 
and da, S. 58° W.; required the angle d. Ans. 151°. 

PROBLEM IX. 

• 

To change the bearings of the sides of a survey in a corre¬ 
sponding manner , so that any particular one of them 
may become a Meridian. 




96 


DIMENSIONS OF A SURVEY. 


CHAP. 1. 


RULE. 

Subtract the bearing of the side that is to be made a 
meridian, from those bearings that are between the same 
points that it is, and also from those that are between 
points directly opposite to them. If it is greater than 
either of the bearings from which it is to be subtracted, 
take the difference and change E. to W., or W. to E. 


Add the bearing of the side which is to be made a me¬ 
ridian, to those bearings which are neither between the 
same points that it is, nor between the points that are 
directly opposite to them. If either of the sums exceeds 
90°, take the supplement and change N. to S., or S. to 



JVote .—When the bearings of some, or all, of the sides 
of a survey have been thus changed, and by calculation 
the changed bearing of another side or line has been 


* The changing of the bearings so as to make a given side become 
a meridian, may be illustrated by means of a protracted survey. 
If a protracted survey or plot is held horizontally with the meridian in 
a north and south direction, the north end being towards the north, 
the bearings of the sides of the plot will then correspond with the 
bearings of the sides of the survey. If then, keeping the paper 
horizontal, it be turned round till any particular side of the plot has a 
north and south direction, or becomes a meridian, the bearings of all 
the other sides of the plot will have been changed by a like quantity. 
But it is evident, that neither the relation of the different parts of the 
plot to one another, the area nor the lengths of the sides will have been 
altered by this change. It may be here observed, that some calcu¬ 
lations in surveying are considerably shortened by changing the bear¬ 
ings so as to make a certain side become a meridian. The method 
was communicated to me by Robert Patterson, late Professor of 
Mathematics and Natural Philosophy in the University of Pennsyl¬ 
vania . 




CHAP. I. 


DIMENSIONS OF A SURVEY. 


97 


found, its true bearing will be obtained by applying to 
the changed bearing, the bearing of the side which was 
made a meridian, in a contrary manner to what is di¬ 
rected in the rule ; that is by adding in the case in which 
the rule directs to subtract, and by subtracting in the 
case in which it directs to add. 

i t 

EXAMPLES. 

1. Given the bearings of the sides of a survey as fol¬ 
low ; 1st. S. 4 5i° W. ; 2nd. N. 50° W. ; 3rd. North; 4th 
N. 85° E.; 5th. S. 47° E.; 6th. S. 20^° W.; and 7th. N. 
51$° W. Required the changed bearings, so that the 
5th side may be a meridian. 

TSt. S. 451° W. 

47 


92 -h 
180 


chang. bear. N. 87£° W. 

f, t t,* ! • (■ 

2nd. N. 50° W. 
47 


chang. bear. N. 3 W. 

3rd. N. 0° E. 
47 


chang. bear. N. 47 E. 

4th. N. 85° E. 
47 


132 

180 

chang. bear. S. 48 E. 
N 








98 


DIMENSIONS OF A SURVEY. 


CHAP. I. 


5th. side, changed bearing, South. 

6th. S. 204 ° W. 

47 


chang. bear. S. 674 W. 

7th. N. 5H° W. 
47 


chang. bear. N. 4£ W. 


2. Given the following barings of the sides of a sur¬ 
vey ; 1st.J3» 404° E.; N. 54° E.; ^d. N. 29^° E.; 4th. 
N. 28f° E.; 5th. N. 57° W.; and 6th, S. 47° W.; to find 
the changed bearings so that the 2nd. side may be a 
meridian. Ans. 1st. N. 854° E. ; 2nd. North; 3rd. N. 
24$° W.; 4th. N. 254° W.; 5th. S. 69° W..: 6th. S. 7° E. 

i 

3. Given the bearings as in the 1st. tf^mple; viz. 
1st. S.454° W.; 2nd. N. 50° W.; 3rd. North; 4th. N. 
85° E.; 5th. S. 47° E.; 6th. S. 204° W.; 7th. N. 511° 
W.; to find the changed bearings so that the 6th. side 
may ^e a meridian. Ans. 1st. S. 25° W.; 2nd. N. 70^° 
W.; 3rd. N. 20^° W.; 4th N. 644° E.; 5th. S. 674° E.; 
6th. South; 7th. N. 711° W. 


PROBLEM X. 


/ 

Of the Bearing , Distance , Difference of Latitude and 
Departure , any two being given, to find the other two. 




CHAP. I. 


DIMENSIONS OP A SURVEY. 


99 


RULE. 

\ i 

When the bearing and distance are given. 

As Rad. : cos. of bearing : : distance : dif. of latitude. 
Rad. : sin. of bearing : : distance : departure. 

When the bearing and difference of latitude are given. 

As Rad. : sec. of bearing : : diff. lat. : distance. 

Rad. : tang, of bearing : : diff. lat. : departure. 

When the bearing and departure are given. 

As Rad. : cosec. of bearing : : departure : distance. 
Rad. : cotang, of bearing : : departure : diff. lat. 

When the difference of latitude and the departure are given. 

As Diff lat. : departure : : rad. : tang, of bearing. 

Rad. : sec. of bearing : : diff lat. : distance. 

When the distance and difference of latitude are given. 

As Diff lat. : distance : : rad. : sec. of bearing. 

Rad. : tang, of bearing : : diff lat. : departure. 

When the distance and departure are given. 

As Distance : departure : : rad. : sin. of bearing. 

Rad. : cos. of bearing : : distance : diff lat. 

JVote. —It is evident the above proportions are the so¬ 
lutions of a right-angled triangle, having for its sides the 
distance, difference of latitude, and departure. 


100 


DIMENSIONS OF A SURVEY. 


CHAP. I. 


EXAMPLES. 

1. Given the bearing of a line, N. 53° 20' E., dist. 

13.25 ch.; to find the difference of latitude and the de¬ 
parture. Ans. Diff. lat. 7.91 N. ; dep. 10.63 E. 

2. Given the bearing of a line, S. 32° 30' E., and the 
departure 10.96 ch. to find the distance and difference 
of latitude. Ans. Dist. 20.40 ch.; diff. lat. 17.20 S. 

7 ' ■ ' • A 

3. Given the distance of a line, running between the 

north and east, 44 ch. and its difference of latitude 34.43 
ch.; to find the bearing and departure. 

Ans. Bearing, N. 38° 30' E.; dep. 27.39 ch. E. 

4. The bearing of a line S. 32° 30' E., and the differ¬ 
ence of latitude 17.21 ch. being given, to find the dis¬ 
tance and departure. Ans . Dist. 20.41 ch.; dep. 10.96 E. 

5. Given the difference of latitude of a line 27.92 N., 

and the departure 5.32 E.; to find the bearing and dis¬ 
tance. Ans. Bearing, N. 10° 47' E.; dist. 28.42. 

6. The distance of a line, running between the north 
and west, is 35.35 ch., and its departure ] 5.08 ch., re¬ 
quired the bearing and difference of latitude. 

Ans. Bearing N. 25° 15' W.; diff. lat. 31.97 N. 


PROBLEM XI. 

To find the difference of latitude and departure corresponding 
to any given bearing and distance , by means of the Tra¬ 
verse Table. 


CHAP. I. DIMENSIONS OF A SURVEY. 101 

* 

RULE. 

When the distance is any number of whole chains or 
perches , not exceeding 100. 

Find the given bearing at the top or bottom of the 
table, according as it is less or more than 45°. Then 
against the given distance, found in the column of dis¬ 
tances at the side of the table, and under or over the 
given bearing, is the difference of latitude and depar¬ 
ture ; which must be taken as marked at the top of the 
table when the bearing is at the top; but as marked at 
the bottom when the bearing is at the bottom. 

When the distance is a number of whole chains or perches, 

exceeding 100. 

Separate the distance into parts that shall not ex¬ 
ceed 100 each; and find as before, the difference of 
latitude and departure, corresponding to the given 
bearing and to each of those parts; the sums of these 
will be the difference of latitude and departure required. 

When the distance is expressed by chains or perches and the 

decimal of a chain or perch. 

Find as above the difference of latitude and depar¬ 
ture corresponding to the given bearing and to the 
whole chains or perches. Then considering the deci¬ 
mal part as a whole number, find the difference of lati¬ 
tude and departure corresponding to it, and remove 
the decimal point in each of them, two figures to the 
left hand if there are two decimal figures in the dis¬ 
tance, or one figure to the left if there is but one; then 


i 


i 


A 

102 DIMENSIONS OF A SURVEY. CHAP. I. 

these added to the former will give the difference of 
latitude and departure required. 

Note. —When the number of whole chains or per¬ 
ches is less than 10, and the second decimal figure is 
a cipher, the difference of latitude and departure may be 
taken out at once, by considering the mixed number, 
rejecting the cipher, as a whole number. The differ¬ 
ence of latitude and departure thus found must have the 
decimal point in each, removed one figure to the left 
hand. 

EXAMPLES. 

1. Given the bearing of a line S. 35£° E., dist. 79 ch. ; 
required the difference of latitude and departure by the 
traverse table. Arts. Diff. lat. 64.51 S.: dep. 45.59 E. 

2. A line bears N. 20£° E., 117 ch.; required the dif¬ 
ference of latitude and the departure. 

Dist. 100, gives diff. lat. 93.67 and dep. 35.02 
17 - 15.92 5.95 

Whole dist. 117 diff. lat. 109.59 N. dep .40.97 E. 

3. Required the difference of latitude and the depar¬ 
ture of a line which bears, S. 41 f° W., 57.36 ch. 

Dist. 57.00 gives diff. lat. 42.53 and dep. 37.96 
.36 - .27 .24 

Whole dist.57.36 diff. lat. 42.80 S. dep. 38.20W. 

4. Required the difference of latitude and departure of 
a line which bears, N. 72° W., 124.37 ch. 

Dist. 100.0 gives diff lat. 30.90 and dep. 95.11 

24.00- 7.42 22.83 

.37- .11 .35 

diff lat.38.43 N. dep.ll8.29W. 


Whole dist. 124.37 















CHAP. I. 


103 


DIMENSIONS OF A SURVEY. 

<s 1 

5. Given the bearing and distance of a line, N. 39^° 

W. 15.20 ch., to find its difference of latitude and depar¬ 
ture. Ans. Diff. lat. 11.72 N., and dep. 9.67 W. 

6. The bearing and distance of a line are N. 46° E., 

27.35 ch.; required its difference of latitude and depar¬ 
ture. Ans. Diff. lat. 18.93 N. and dep. 19.60 E. 

7. The bearing and distance of a line are S. 374° W., 

137.50 ch.; required its difference of latitude and depar¬ 
ture. Ans. Diff lat. 109.45 S., and dep. 83.23 W. 

„ l K V „ I ' " 

8. Required the difference of latitude and departure 

of a line, whose bearing and distance are S. 6^° E., 5.60 
ch. Ans. Diff lat. 5.56 S., and dep. 0.63 E. 


PROBLEM XII. 

Given the bearings and distances of all the sides of a trad of 
land to obtain the corrected latitudes and departures. 

RULE. 

< 

1. Rule a table as in the annexed example, in the first 
vertical column of which, place the letters designating 
the sides, or the numbers denoting the stations at the be¬ 
ginning of each side; in the second column, place the 
bearings; and, in the third, the distances. 

2. Find, by the last problem, the difference of latitude 
and the departure, corresponding to each side, and 
place them in the next four columns, under their proper 
heads of N. or S., E. or W. Add up the northings 


104 DIMENSIONS OF A SURVEY. CHAP. I. 

*V ‘l , y \ 

and southings, and if the sums are not equal, find their 
difference, which will be the error of the survey in differ¬ 
ence of latitude; which call by the same name as the 
least sum. Proceed in the same manner with the east¬ 
ings and westings, and find the error in departure. 
Also add up the column of distances. Then it will be, 

„ As the sum of the distances, 

* . * \ 

Is to any particular distance, 

So is the error in latitude or departure 

To the correction of latitude or departure, corres¬ 
ponding to that distance. 

3. Find, by the above proportion, the corrections of 
latitude and departure corresponding to all the sides, 
calculating them to the nearest two decimal figures, 
and place them in the next two columns, heading them 
with the names of the errors in latitude and departure. 
If the sums of these corrections, are not respectively 
equal to the errors in latitude and departure, which, in 
consequence of the fractions neglected, will sometimes 
be the case, alter some of them by a unit in the second 
decimal figure, to make them so. 

4. Apply these corrections to their corresponding dif¬ 
ferences of latitude and departures, by adding when of 
the same name, but by subtracting when of different names, 
and the corrected differences of latitude and departures 
will be obtained; which may be placed in the four suc¬ 
ceeding columns. 

In these the sums of the northings and southings will 
be equal, and also those of the eastings and westings.* 


* The directions given in the rule, for correcting the errors in 
difference of latitude and departure, a,re deduced from the rule 





CHAP, I. 


DIMENSIONS OF A SURVEY. 


105 


Note 1.—In the proportion for finding the correction 
of the latitude or departure, the decimal parts of the 
sum of the distances and of the particular distance may 
be omitted, taking in each case, the nearest number of 
whole chains. 

2. The corrections may be frequently estimated with 
sufficient accuracy without the trouble of working out 
the proportions. 

3. When one or two of the sides are hilly, or when 
there are other difficulties in the way of obtaining their 
bearing or distances with accuracy, it is better to allow 
a considerable part of the errors, on the latitudes and 
departures corresponding to them, and afterwards to 
apportion the remaining part among the others. 

'• EXAMPLES. 

1. Given the bearings and distances of the sides of a 
tract of land as follow: 1st. S. 40|° E. 31.80 ch.; 2nd. 
N. 54° E. 2.08 ch.; 3rd. N. 29i° E. 2.21 ch.; 4th. 
N. 281° E. 35.35 ch.; 5th N. 57° W. 21.10 ch.; 6th. S. 47° 
W. 31.30 ch. Required the corrected differences of 
latitude and departures. 


Sta. 

Courses. 

Dist. 

Ch. 

N.L. 

S.L. 

E. D. 

W.D. 

Cor 

S. 

Cor 

E. 

N. L. 

1 S. L. 

E. D. 

W.D. 

1 

S. 40}E. 

31.80 


24.18 

20.65 


.03 

<05 


24.21 

20.70 


2 

N. 54 E. 

2.08 

1.23 


1.68 


.00 

.00 

1.23 


1.68 


3 

N. 29-} E. 

2.21 

1.92 


1.08 


.00 

.00 

1.92 


1.08 


4 

N. 28fE. 

35.35 

31.00 


17.00 


.04 

.05 

30.96 


17.05 


5 

N. 57 W. 

21.10 

11.49 



17.69 

.02 

.03 

11.47 



17.66 

6 

S. 47 W. 

31.30 


21.34 


22.89 

.03 

.04 


21.37 


22.85 


1 

123.84 

45.64 

45.52 

40.41 

40.58 

.12 

.17 

45.58 

45.58 

40.51 

40.51 


45.5*2 40.41 

.12 Er. S. .17 Er. E. 

given and demonstrated in No. 4, of a periodical work, called the 
Analyst, by Nathaniel Bowditch , A. M., and also by the editor Robert 
Adrain. The demonstration is too long, and not of a nature for in¬ 
sertion here. 

O 



















































































































106 


DIMENSIONS OF A SURVEY. 


CHAP. I. 


As 124 . 

32 : 

: .12 : 

.03 

As 124 : 

32 

: .17 : 

.04 or 05.* 

124 : 

2 : 

: .12 : 

.00 

124 : 

2 

: .17 : 

.00 

,124 : 

35 : 

: .12 : 

.03 or .04 

124 : 

35 

: .17 : 

.05 

124 : 

21 : 

: .12 : 

.02 

124 : 

21 

: .17 : 

.03 

124 : 

31 : 

: .12 : 

.03 

124 : 

31 

: .17 : 

.04 


2. Given the bearings and distances of the sides of a 
tract of land as follow: 1st. N. 75° E. 13.70 ch.; 2nd. 
N. 204 E. 10.30 ch.; 3rd. East 16.20 ch.; 4th. S. 334° 
W. 35.30 ch.; 5th. S. 76 W. 16 ch.; 6th. North 9 ch.; 
7th. S. 84° W. 11.60 ch.; 8th. N. 534° W. 11.60 ch.; 
9th. N. 364° E. 19.36 ch.; 10th. N. 224° E. 14 ch.; 11th. 
S. 76|° E. 12 ch.; 12th. S. 15° W. 10.85 ch.; 
13th. S. 18° W. 10.62 ch.; to the place of beginning. 
Required the corrected latitudes and departures. 

Ms. 1st. 3.56 N. 13.26 E.; 2nd. 9.66 N. 3.62 E.; 
3rd. 0.02 N. 16.22 E.; 4th. 29.39 S. 19.44 
W.; 5th. 3.85 S. 15.50 W.; 6th. 9.01 N. 
0.01 E.; 7th. 1.19 S. 11.52 W.; 8th. 6.96 
N. 9.27 W.; 9th. 15.54 N. 11.61 E.; 10th. 
12.95 N. 5.38 E.; 11th. 2.73 S. 11.70 E.; 
12th. 10.46 S. 2.80 W.; 13th. 10.08 S. 
3.27 W. 


* When, as in this case, the correction is found to be nearly mid¬ 
way between two numbers, it is best to note them both. Then, if in 
using the one that is nearest to the true value, the sum of the cor¬ 
rections does not equal the whole error, the other should be taken. 








CHAPTER H. 


On supplying omissions in the dimensions of a survey. 

When the bearings and distances of all the sides of a 
survey are known, except one bearing and one distance, 
or two bearings, or two distances, these can be obtained 
by calculation, provided those that are known can be 
depended on, as sufficiently accurate. This may some¬ 
times be necessary when there are obstacles in the way 
of obtaining one or two of the bearings or distances; or 
when, after they have all been taken on the ground, the 
notes of one or two of them happen to be obliterated. 
As however a bearing or distance thus obtained, must 
be affected by any error or errors that may have been 
made in taking the others, it is better, when practicable, 
to have the bearings and distances of all the sides, as 
taken on the ground. 

PROBLEM I. 

The bearings and distances of all the sides of a tract of land , 
except the bearing and distance of one side , being given, to 
find these. 

RULE. 

Find by prob. 11, of the preceding chapter, the differ¬ 
ences of latitude and the departures for the sides whose 
bearings and distances are given, and place them in 
their proper columns in a table ruled for the purpose; 
Add up the northings and southings, and taking the dif- 


108 


SUPPLYING OMISSIONS. 


CHAP. II. 


ference of their sums, place it opposite the unknown 
side, in the column whose sum is the least. The sums 
of the two columns will then be equal. This is called 
balancing the latitudes. Do the same with the eastings 
and westings. The two numbers inserted to make the 
latitudes and the departures balance, will be the dif¬ 
ference of latitude and the departure of the unknown 
side; with which its bearing and distance may be found, 
by prob. 10, of the preceding chapter. 

Note 1.—By the application of this rule, the bearing 
and distance of a line joining two corners or stations, 
may be found, when there are obstacles in the way which 
prevent our going directly from one corner to the other, 
or when one cannot be seen from the other. To do this, 
let one or two, or more stations, if necessary, be taken 
out of the line, and take the bearing and distance from 
the first corner to the first assumed station; from this 
station to the second; and so on, to the second corner. 
Then considering these bearings and distances, as the 
bearings and distances of the sides of a survey, the re¬ 
quired bearing and distance of the line may be found 
by the above rule. The bearing thus found must be 
reversed , in order to have the bearing from the first cor¬ 
ner to the second. 

2. In the same way the bearing and distance of a 
straight road to run between two given places, may be 
found, by taking the several bearings and distances of 
the old road if there is one; or of lines joining assu¬ 
med stations and extending from one place to the other. 

EXAMPLES. 

1. The bearings and distances of the side of a tract 
of land, except the bearing and distance of one side 


CHAP. II. 


SUPPLYING OMISSIONS. 


109 


which are not known, are as in the following field-notes ; 
required the unknown bearing and distance. 



Ch. 

1. S. 45* W. 15.16 

2. N. 50 W. 22.10 

3. North 18.83 

4. N. 85 E 35.65 

5. - - 

6. S. 20* W. 23.80 

7. N. -51| W. 26.47 


Sta. 

Bearings. 

Dist. 

N. 

s. 

* 

E. 

w. 

1 

S. 45* W. 

15.16 

• 

10.62 

« 


10.81 

2 

N. 50 W. 

22.10 

14.20 



16.93 

3 

North 

18.83 

18.83 




4 

N. 85 E. 

35.65 

3.11 

» 


35.52 


5 




(19.79) 

(21.20) 


6 

S. 20* W. 

23.80 


22.29 


8.33 

7 

N. 51* W. 

26.47 

16.56 



20.65 




52.70 

52.70 

56.72 

56.72 


As diff. of lat. 19.79 S. Ar. Co. 8.70355 
: dep. 21.20 E. - - 1.32674 

:: rad. ----- 10.00000 


: tang. bear. S. 47° E. 


10.03029 


As rad.. 

: sec. bearing 47° 

:: diff. lat. 19.79 - 


10.00000 

10.16622 

1.29645 


dist. - 29.02 - 

Ms. S. 47° E. 29.02 ch. 


1.46267 





































































110 


SUPPLYING OMISSIONS. 


CHAP. II. 


2 . Given the bearings and distances of the sides of a 
tract of land, as follow: 1 st. N. 151 W. 9.40 ch.; 2 nd. 
N. 63f E. 10.43 ch.; 3rd. S. 49° E. 8.12 ch.; 4th. S. 134 
E. 8.45 ch.; 5th. S. 161 E. 6.44 ch.; 6 th. unknown; 
7th. N. 60° W. 9.72 ch. ; 8 th. N. 174 E. 7.65 ch.; re¬ 
quired the bearing and distance of the 6 th side. 

Ans. S. 60° 8 ' W. 12.27 ch. 

3 . One side of a tract of land of which a survey is to 

be taken, passes through a pond. Two stations are 
therefore taken on one side of the pond as represent¬ 
ed in Fig. 80. The bearings and distances from the 
first end of the side to the first station, from that to the 
second, and thence to the other end of the side are; 1 st. 
S. 52° W. 10.70 ch.; 2 nd. S. 7 4 0 W. 13.92 ch.; and 3rd. 
S. 334 E. 9 ch. Required the bearing and distance of 
the side. Ans. S. 10 ° 47' W. 28.42 ch. 

4. Given the bearings and distances of an old road, 

running between two places* as follow; 1 st. S. 10 ° E. 
92.20 ch. ; 2 nd. S. 15° W. 120.50 ch. ; 3rd. S. 181 
W. 2.05 ch. ; 4th. S. 71 1 E. 68 dh. Required the bear¬ 
ing and distance of a straight road, that shall connect 
the two places. Ans. S. 2 ° 8 ' W. 423.47 ch. 

PROBLEM II. 

Given all the bearings and distances of the sides of a survey , 

* except the distances of two sides , to find these. 

RULE. 

By prob. 9, of the preceding chapter, change all the 
given bearings, in a corresponding manner, so that one 
of the sides whose bearings only are given, may become 
a meridian. With the changed bearings and given dis¬ 
tances find the corresponding differences of latitude 
and departures. Add up the eastings and westings, 
and take the difference of their sums, which will be the 


CHAP. 11. 


SUPPLYING OMISSIONS. 


Ill 


departure of the unknown side, that is not made a 
meridian. With this departure and the changed bear¬ 
ing, find by prob. 10, of the preceding chapter, the 
distance and difference of latitude of this side, which 
place in their proper columns. Now add up the north¬ 
ings and southings, and take their difference, which 
will be the distance of the side, made a meridian.* 

EXAMPLES. 

Given the following bearings and distances of the 
sides of a survey; 1st. S. 45£ W. 15.16 ch. : 2nd. N.50° 
W. 22.10 ch. ; 3rd. North, 18.83 ch. ; 4th. N. 85° E. 
35.65 ch.; 5th. S. 47° E. dist. unknown; 6th. S. 20£ W. 
dist. unknown; 7th. N. 51 f W. 26.40 ch. to the place 
of beginning. Required the unknown distances. 


Sta. 

Bearings. 

Changed 

bearings. 

Dist. 

N. 

S. 

E. 

W. 

1 

S 45|°W. 

N87^°W. 

15.16 

0.66 



15.15 

2 

N. 50 W. 

N. 3 W. 

22.10 

22.07 



1.16 

3 

North. 

N. 47 E. 

18.83 

12.85 


13.77 


4 

N. 85 E. 

• 

S. 48 E. 

35.65 

% 

23.85 

26.49 


5 

S. 47 E. 

South 

(29-02) 


(29.02) 



6 

S 20£ W. 

S 67^ W. 

(23-80) 


(9.11) 


(21.99) 

7 

N.5HW. 

N. 4* W. 

26.47 

26.40 



1.96 





61.98 

61.98 

40.26 

40.26 


* The reason of the rule is obvious. For as the side made a me¬ 
ridian has no departure, the difference of the sums of the departures, 
must be the departure of the other unknown side. And when the 
difference of latitude of this side has been found and placed in its 
proper situation, the difference of the sums of the latitudes must evi¬ 
dently be the difference of latitude of the side made a meridian ; or, 
which in this case is the same thing, its distance. 
















































































112 SUPPLYING OMISSIONS. 

CHAP. II. 

As rad. - 

_ 

10.00000 

: cosec. chang. bearing 

67£° 

10.03438 

: : dep. 

21.99 

1.34223 

: Dist 6th. side 

23.80 

1.37661 

As rad. - 

«• — 

10.00000 

: cotang, chang. bearing 

674° - 

9.61722 

: : dep. - 

21.99 

1.34223 

: diff lat. 6th. side 

9.11 

0.95945 


Ans. 5th. side 29.02 ch. and 6th. side 23.80 ch. 


2. Given the bearings and distances of a tract of land 
as follow: 1st. S 40£ E. 31.80 ch.; 2nd. N. 54° E. dist. 
unknown; 3rd. N. 29f E. 2.21 ch.; 4th. N. 28£ E. 35.35 
ch.; 5th. N. 57° W.dist. unknown; 6th. S. 47° W. 31.30 
ch.; to the place of beginning. Required the distances 
of the 2nd. and 5th .sides. 

Ans . 2nd. side, 2.08 ch. and 5th. side 20.90 ch. 

PROBLEM III. 

Given the bearings and distances of all the sides of a survey , 
except two ; one of which has only its bearing given , and 
the other , the distance and the points of the compass be¬ 
tween which it runs; to find the unknown bearing and 
distance. 


RULE. 

As in the last problem, change all the given bearings, 
so that the side whose bearing only is given, may be¬ 
come a meridian. Find the differences of latitude and 
the departures, corresponding to the changed bearings 
and the given distances. Take the difference of the 
sums of the eastings and westings, which will be the de- 




CHAP. II. 


SUPPLYING OMISSIONS. 


113 


parture of the side whose bearing is not given. With 
the given distance and this departure, find, by chap. 1. 
prob. 10. the changed bearing and difference of latitude, 
and place them in their proper columns. From the 
changed bearing, the true bearing may be readily found 
by note to prob. 9. chap. 1. Lastly, take the difference 
of the sums of the northings and southings, and it will 
be the distance of the side, changed to a meridian. 

a* ' 

Note .—The changed bearing as found by the rule, 
must be reckoned from the north , or the south point of the 
compass, according as the one, or the other, will ren¬ 
der the true bearing when found from it, conformable to 
the given points. The point from which the changed 
bearing must be reckoned determines also the column 
in which the difference of latitude must be placed. 
Sometimes the changed bearing when reckoned from 
either north or south, will render the true bearing con¬ 
formable to the given points. In such cases, there are 
two different bearings and distances that will answer 
the conditions of the problem; and we can only know 
which of them is the right one by previously knowing 
the required bearing nearly. 

EXAMPLES. 

1. Given the bearings and distances of a survey as fol¬ 
low : 1st. S. unknoivn W. 15.16 ch.; 2nd. N. 5Q° W. 
22.10 ch.; 3rd. North 18.83 ch.; 4th. N. 85° E. 35.65 
ch.; 5th. S. 47° E. 29.02 ch.; 6th. S 20| W. dist. un¬ 
known ; 7th. N. 51i° W. 26.47 ch. Required the un¬ 
known bearing and distance. 

P 


\ 


114 


SUPPLYING OMISSIONS. CHAP. II. 


Sta. 

Bearings. 

Changed bear¬ 
ings. 

Dist. 

N. 

S. 

E. 

W. 

1 

S.(45°36')W. 

(S.25° 6'W.) 

15.16 


13.73 


(6.43) 

2 

N. 50 W. 

N. 70^ W. 

22.10 

7.37 

• 


20.83 

3 

North 

N. 20 \ W. 

18.83 

17.64 



6.59 

4 

N. 85 E. 

N. 64^ E. 

35.65 

15.35 


32.18 


5 

S. 47 E. 

S. 67£ E. 

29.02 

\ 

0 

11.11 

26.81 


6 

S. 20£ W. 

South 

(23.81) 


(23-81) 

• 


7 

N. 51£ W. 

N. 71f W. 

26.47 

8.29 



25.14 





48.65 

48.65 

58.99 

58.99 


As dist. 1st. side 15.16 Ar. Co. 8.81930 
: dep. do. 6.43 0.80821 

: : rad.. 10.00000 


: dep. do. 6.43 0.80821 

: : rad.. 10.00000 


sin. chan. bear. 25° 6' - - 9.62751 

As rad.. 10.00000 

: cos. chang. bearing 25° 6' 9.95692 

: : dist. - - 15.16 1.18070 

t , ‘l ~ 

: diff. lat. - - 13.73 1.13762 


Am. 1st. S. 35° 36' W. 6th. 23.81 ch. 

2. Given the following bearings and distances of a sur¬ 
vey : 1st. S. 40i° E. 31.80 ch.; 2nd. N. 54° E. dist. un¬ 
known ; 3rd. N. 29i E. 2.21 ch. ; 4th. N. unknown E. 
35.35 ch.; 5th. N. 57° W. 20.90 ch.; 6th. S. 47° W. 
31.30 ch. to place of beginning. Required the bearing 
of the 4th. side and distance of the 2nd. side. 

Ans. Bearing of 4th. side N. 281° E.; dist. of 2nd 
side, 2.09 ch. 

































































CHAP. II. 


SUPPLYING OMISSIONS. 


115 


PROBLEM IV. 

'*■*- l" ' / ' f ' * 

Given all the bearings and distances of the sides of a tract 
of land , except the bearings of two sides , to find these 
bearings. 

, RULE. 

v) “ ■ ; *•' !'.?• 

1. Find the difference oflatitude and the departure of 
each side, whose bearing and distance are both given. 
Take the difference of the sums of the northings and 
southings of these sides, and also the difference of the 
sums of the eastings and westings. These differences 
will be the difference of latitude and the departure of a 
line, which with those sides would form a closing sur¬ 
vey ; and which may therefore be called a closing line . 

2. With the difference of latitude and departure of 
the closing line find, by prob. 10. chap. 1, its bearing and 
distance. Take the closing line and the two sides 
whose bearings are not given, for the three sides of a 
triangle, and calculate the angles. 

3. To the bearing of the closing line, apply by addi¬ 
tion or subtraction, as the case may require, the angle 
contained between it, and the side which is the one, 
coming first in the order of the survey; and it will give 
the bearing of that side. Then to the reverse bearing 
of that side, apply in a proper manner, the angle con¬ 
tained between the two sides which are sides of the sur¬ 
vey, and it will give the bearing of the second of those 
sides.* 


* It is easy to see the reason of the rule, by considering that the 
two sides whose bearings are not given, being made to form with 





116 


J 


SUPPLYING OMISSIONS. 


CHAP. II. 


EXAMPLES. 

J . \ i < 

1. Given the bearings and distances of the sides of a 
tract of land as follow : 1st. S. unknown W. 15.16 ch.; 
2nd. N. 50° W. 22.10 ch.; 3rd. North 18.83 ch.; 4th. N. 
85° E. 35.65 ch.; 5th. S. unknown E. 29.02 ch.; 6th. S. 
20£° W. 23.80 ch.; and 7th. N. 51? W. 26.47 ch. Re¬ 
quired the unknown bearings. 


Sta. 

Bearings. 

Dist. 

N. 

s. 

\ * 

E. 

w. 

1 

s. w. 

15.16 



< 


2 

N. 50° W. 

22.10 

14.20 



16.93 

3 

North 

18.83 

18.83 




4 

N. 85 E. 

35.65 

3.11 


35.52 


5 

S. E. 

29.02 




• V « 

6 

S. 204 W. 

23.80 


22.29 


8.33 

7 

N. 514 W. 

26.47 

16.56 



20.65 



4 

52.70 

22.29 

35.52 

45.91 


30.41 S. 10.39 E. 


the closing line, the sides of a triangle, the sum or difference of their 
differences of latitude, will necessarily be equal to the difference of lati¬ 
tude of the closing line ; and that, therefore, their differences of lati¬ 
tude will be such as to make the sums of the northings and southings 
of the whole survey equal; and the same for the departures. 







































































CHAP. II. 


SUPPLYING OMISSIONS. 


117 


As diff. lat. 
: dep. 

:: rad. 


, /=-* 


30.41 S. 
10.39 E. 


Ar. Co. 8.51698 
1.01662 
10.00000 


tang of bear, of clos. line, S. 18° 52' 


9.53360 


As rad..’ - 10.00000 

: diff. lat. - - - 30.41 - 1.48302 

:: sec. of bear, of clos. line 18° 52' - 10.02398 


: dist. of clos. line - 32.14 


1.50700 


Let D E, Fig. 78, represent the closing line, D F, the 
1st. side of the survey, and F E, the 5th. side. Then, 

D E 32.14 

D F 15.16 Ar. Co. 8.81930 

F E 29.02 - 8.53730 

2)76.32 


Half sum 38.16 
Remainder 6.02 


log. 1.58161 
— 0.77960 


cos. 4 F 43° 44' 2)19.71781 


F 87 28 9.85890 


As D E 

32.14 

Ar. Co. 8.49295 

: F E 

29.02 

1.46270 

: : sin. F 

87° 28' 

4 

9.99958 

: sin. D 

64° 26' 

* 

9.95523 

DE, S. 

t—i 

00 

o 

Or 

to 

W 

F D, N 45° 34' E 

Angle D 

64 26 

Angle F 87 28 


1st side, S. 45 34 W. 

I 


133 2 

180 00 


5th side, S. 46 58 E. 















118 


CONTENT OF LAND. 


CHAP. III. 


2. Given the bearings and distances of the sides of a 
tract of land as follow: 1st. S. unknown E. 31.80 ch.; 
2nd. N. 54° E. 2.08 ch.; 3rd. N. 29* E. 2.21 ch.; 
4th. N. 281° E. 35.35 ch.; 5th. N. 57° W 20.90 ch.; 
and 6th S. unknown W. 31.30 ch. to the place of begin¬ 
ning. Required the unknown bearings. 

Jins. 1st. S. 40*° E.; and 6th. S. 47° 1' W. 


CHAPTER 111. 

Problems for finding the Content of Land. 

When the sides of a survey are right lines, and all the 
bearings and distances are given, the area may be found 
by a problem that will be given in this chapter. If one 
or two of the bearings or distances are not known, they 
may be found by the problems in the last chapter. Al¬ 
though the problem alluded to, is general, and may be 
applied whatever number of sides there may be, yet 
there are some particular rules for finding the areas of 
triangles and quadrilaterals, which are often useful. 
These and also rules for finding the areas of circles 
and ellipses are given in the first part of the chapter. 

When a part of the boundary of a tract of land, is 
irregular, as is frequently the case, when one or more 
of the sides are bounded by water, it is sometimes very 
troublesome to take all the bearings and distances re¬ 
quisite to obtain the area with accuracy. In these 
cases, it is usual to run one or more straight lines, 
called stationary lines, near to such boundary, and so 
as to connect the straight sides of the survey. In mea¬ 
suring these stationary lines, perpendicular distances 
are measured from them, to each bend in the irregular 
boundary. These perpendicular distances are called 


CHAP. III. 


CONTENT OF LAND. 


119 


off-sets . The lengths of the off-sets, and the distance of 
the foot of each, from the commencement of the sta¬ 
tionary line, should be carefully noted in the field book; 
observing also that such a number of off-sets should be 
taken, that the part of the irregular boundary intercept¬ 
ed between each adjacent two, may, without material 
error, be considered a straight line. From these notes, 
the area or areas of the land contained between the 
stationary line or lines, and the irregular boundary, may 
readily be calculated. This area added to the area 
enclosed by the stationary lines, and straight sides of 
the survey, when they are on the outside of the station¬ 
ary lines, or subtracted from it, when on the inside, 
will give the area of the survey. 


In those cases, in which water is a boundary of a 
tract of land, if that water is a brook or rivulet, it is 
usual to consider a line running through its middle as 
the true boundary; and the off-sets must be measured 
accordingly. When tide water is the boundary, the 
land is considered as extending to the line of low water 
mark. 


If the bearings of all the corners of a tract of land 
from two stations taken either within or out of the tract 
are given, and also the bearing and distance of these 
stations from each other, the area may be calculated. 
It is however necessary that the two stations should 
be so taken that they shall not be in a straight line, or 
very nearly in a straight line, with either of the corners 
of the land. This method of obtaining the area, though 
not practically so accurate as where the bearings and 
distances of the sides are correctly given, may some¬ 
times be found useful. 

Some surveyors, in order to calculate the area of a 


120 


CONTENT OF LAND. 


CHAP. III. 


survey, first protract it; then dividing the plot into tri¬ 
angles and trapeziums by lines joining opposite cor¬ 
ners, they measure with the scale and dividers, the 
lengths of such lines and perpendiculars as are requi¬ 
site for calculating the areas of these.' The sum of the 
areas thus obtained, is the area of the survey. When 
the survey is carefully protracted, and proper attention 
- is given to take the measures with the utmost precision, 
this method serves to give a near value of the content; 
but is by no means to be depended on as equally ac¬ 
curate with the general problems mentioned above. 

The area of a field or small tract of land, the corners 
of which can be seen from one another, may readily be 
found by means of the chain only. To do this the lengths 
of the sides must be measured, and also the length of 
diagonals joining opposite corners, so as to divide the 
field into triangles. Or instead of the diagonals, the dis¬ 
tances from some assumed point within the field, to the 
several corners, may be used. Having then all the sides 
of the several triangles, the area of each may be found; 
and the sum of these areas will be the area of the tract. 

PROBLEM I. 

To find the area of a Parallelogram , whether it be a Square , 
a Rectangle , a Rhombus , or a Rhomboides. 

RULE. 

Multiply the length by the height or perpendicular 
breadth, and the product will be the area.* 

* Demonstration. Let ABCD (Fig. 68) be a rectangle; and 
let its length AB and CD, and its breadth AD and BC, be each 
divided into as many equal parts, as are expressed by the number 
of times they contain the lineal measuring unit; and let all the 
opposite points of division be connected by right lines. Then, it 




CHAP. Ill, CONTENT OF LAND. 121 

\ ' 

ecause the length of* a square is equal to its 
height, its area will be found by multiplying the side by 
itself. 

EXAMPLES. 

1. Required the area of a square field, a side of 
which measures 7.29 four-pole chains. 

Ch. 

7.29 

7.29 


656 J 

1458 

5103 


10)53.1441 Area 5 A. 1R. 10 P. 

• • 

5.31441 

4 


1.25764 

; 40 ' 

* 

10.30560 

2. Required the area of a rectangular field whose 
length is 13.75 chains, and breadth 9.5 chains. 

is evident lliat these lines divide the rectangle into a number of 
squares, each equal to the superficial measuring unit; and that 
the number of these squares is equal to the number of lineal mea¬ 
suring units in the length, as often repeated as there are lineal 
measuring units in the breadth, or height; that is, equal to the 

i 

length drawn into the breadth. But the area is equal to the num¬ 
ber of squares or superficial measuring units; and therefore the area 
of a rectangle is equal to the product of the length and breadth. 

Again, a rectangle is equal to any oblique parallelogram of an 
equal length and perpendicular height (36.1 ;) therefore the area 
of every parallelogram is equal to the product of its length and height. 

Q 








122 


CONTENT OF LAND. 


CHAP. III. 


13.75 

9.5 

6875 s 

12375 

— 

10)130.625 Area 13 A. 0 R. 10 P. 


13.0625 
4 


.2500 

40 


10.0000 

3. Required the area of a field, in the form of a rhom- 
boides, whose length AB is 42.5 perches, and perpen¬ 
dicular breadth CD is 32 perches. Fig. 15. 

f- 

42.5 

32 


850 

1275 


4|0)136|0.0 

4)34 


8 A. 2 R. 

4. What is the area of a square tract of land, whose 
side measures 176.4 perches? Ans. 194 A. 1 R 36.96 P. 

5. What is the area of a rectangular plantation whose 
length is 52.25 chains, and breadth 38.24 chains ? 

r Ans. 199 A. 3 R. 8.6 P. 

6. The length of a field, in the form of a rhombus, 
measures 16.54 chains, and the perpendicular breadth 
12.37 chains: required the area. Ans. 20 A. 1 R. 33.6 P. 











CHAP. III. 


CONTENT OP LAND. 


123 


7. Required the area of a field in the form of a rhom- 
boides, whose length is 21.16 chains, and perpendicular 
breadth 11.32 chains. Ans. 23 A. 3 R. 32.5 P. 

PROBLEM II. 

jl' t. • , 9 v A ' fc • - 1 V'/ n 

To find the area of a triangle when the base and perpendicu¬ 
lar height are given. 

RULE. 

Multiply the base by the perpendicular height, and 
half the product will be the area.* 

EXAMPLES. 

1. The base AB of a triangular piece of ground, 
measures 12.38 chains, and the perpendicular CD 6.78 

chains: required the area. Fig. 49. 

Ch. 

12.38 

6.78 


9904 

8666 

7428 

2)83.9364 

10)41.9682 Area, 4 A. 0 R. 31 P. 

4.19682 

4 

.78728 


31.49120 


* Demonstration. A triangle is half a parallelogram of the same 
base and altitude, (41.1) and therefore the truth of the rule is evident. 











124 


CONTENT OF LAND. 


CHAP. III. 


2. Required the area of a triangular field, one side 
of which measures 18.37 chains, and the distance from 
this side to the opposite angle 13.44 chains. 

Ans. 12 A. 1 R. 15 P. 

3. What is the area of a triangle whose base is 49 
perches and height 34 perches ? Ans. 5 A. 0 R. 33 P. 

~ i ' 

PROBLEM III. 

To find the area of a triangle when two sides and their in¬ 
cluded angle are given. 

' \ 

RULE. 

As radius, 

Is to the sine of the included angle; 

So is the rectangle of the given sides, 

To double the area.* 

EXAMPLES. 

1. In a triangular lot of ground ABC, the side AB 
measures 64 perches, the side AC 40.5 perches, and 
their contained angle CAB 30°: required the area. 
Fig. 49. 


* Demonstration. In the triangle ABC, Fig. 49. let AB and AC 
be the given sides, including the given angle A, and let CD be perpen¬ 
dicular on AB. Then by trig. rad. : sin. A :: AC : CD ; but (cor. 
1.6) AC : CD :: AC X AB : CD X AB ; therefore (11.5.) rad. : 
sin. A :: AC X AB : CD X AB ; but CD X AB is equal to twice 
the area of the triangle : hence the truth of the rule is evident. 




CHAP. III. 


CONTENT OF LAND. 


125 


As radius - 
v Is to sin. A. 30° - 

So is AB, AC, \ K 

i 40.5 


10.00000 

9.69897 

1.80618 
1.60746 

13.11261 


To double the area 1296 perches 3.11261 

4|0)64|8 
4)16 8 . " 

4 A. 0 R. 8 P. 


2. What is the area of a triangle two sides of which 
measure 15.36 chains and 11.46 chains respectively, 
and their included angle 47° 30' ? Ans. 6 A. 1 R. 38 P. 

3. One side of a triangular field bears N. 12° E. dis¬ 

tance 18.23 chains, and at the same station the other 
adjacent side bears N. 78° 30' E. distance 13.84 chains : 
required the area. Ans. 11 A. 2 R. 11 P. 


4. Required the area of a triangular piece of ground, 
one side of which bears N. 82° 30' W. dist. 19.74 chains 
and at the same station, the other adjacent side S. 24° 
15' E. dist. 17.34 chains. > Ans. 14 A. 2 R. 8 P. 

PROBLEM IV. 

To find the area of a triangle when one side and the two ad¬ 
jacent angles are given. 

• % 

RULE. 

Subtract the sum of the two given angles from 1 Soo¬ 
the remainder will be the angle opposite the given 
side. Then, 








126 


CONTENT OF LAND. 


CHAP. III. 


As the rectangle of radius and the sine of the angle 
opposite the given side, 

Is to the rectangle of the sines of the other angles, 
So is the square of the given side, 

To double the area.* 1 


EXAMPLES. 

- 1. In a triangular field ABC, the side AB measures 
76 perches, the angle A 60°, and the angle B 50°: re¬ 
quired the area. Fig. 47. 


The angle ACB=180° — the sum of the angles A 
and B,=70°. 


As rad. X sin. C, 

: sin. A X sin. B, 

: : AB 2 =ABx AB 


$ rad. 

I sin. C. 70° 
( sin. A. 60° 
( sin. B. 50° 
\ AB 76 
( AB 76 


: double area in perches 4078 

-—. 

v ' 40)2039 






4)50 39 


Ar. Co. 0.00000 
Ar. Co. 0.02701 
9.93753 
9.88425 
1.88081 
1.88081 


3.61041 


12 A. 2 R. 39 P. 






* Demonstration. Let AB, Fig. 49, be the given side of the 
triangle ABC, and A and B the given angles ; also let CD be perpen¬ 
dicular on AB : Then by trig. 

sin. ACB : sin. B : : AB : AC 
rad. : sin. A : : AC : CD. 

Therefore (C.6) rad. X sin. ACB : sin. A X sin. B : : AB X 
AC : CD X AC : : (cor. 1.6) AB : CD : : AB 2 : AB X CD ; 
but AB X CD is equal to double the area of the triangle ABC : 
therefore (1L5) rad. x sin. ACB : sin. A X sin. B : : AB 2 : dou¬ 
ble the area of the triangle ABC. 









) 




CIIAP. III. CONTENT OF LAND. 127 

2. Onfe side of a triangle measures 24.32 chains, and 
the adjacent angles are 63° and 74°: required the area. 

> Jins. 37A. OR. 22P. 

3. What is the area of a triangular field, one side of 

which is 17.36 chains, and the adjacent angles 37° 30' 
and 48° 15' ? Am, 6 A. 3 R. 18 P. 

* 

PROBLEM V. 

v, ~ ■ . 

To find the area of a triangle when the three sides are given, 

I j 

RULE. 

) 

From half the sum of the three sides subtract each 
side severally; multiply the half sum and the three re¬ 
mainders continually together, and the square root of 
the last product will be the area.* * 


* Demonstration. Let ABC, Fig. 69, be the triangle. Bisect 
any two of the angles, BAC, ABC, by the straight lines AG, BG, 
meeting in G ; let fall on the three sides of the triangle, the perpen¬ 
diculars GD, GF, GE, and join GC ; also produce AB, AC, and bi¬ 
sect one of the exterior angles, HBC, by the line BK, meeting 
AG* produced in K, join KC, and let fall the perpendiculars 
KH, KM, and KL. Then (26.1) AD is equal to AE and DG to 
GE ;• also BD is equal to BF, and DG to GF ; hence GF and GE 
are equal, and consequently (47.1) CF is equal to CE. In like 
manner it may be proved that AH is equal to AL, BH to BM 
and CM to CL ; as likewise that KH, KM, # and KL are equal to 
each other. Now since BH is equal to BM and CL to CM, it is 
manifest that AH and AL together, are equal to the sum of the 
three sides AB, AC, and BC ; hence AH or AL is equal to the 

• 

* The angle BAC is less than the angle HBC (16.1;) consequently BAG is 
less than HBK, and BAG, KBA, are together less than HBK, KBA; but HBK, 
KB A, are together equal to two right angles; hence BAG, KBA, are less than 
two right angles; therefore (cor. 29.1) the line BK will meet the line AG pro¬ 
duced. 






m 


128 CONTENT OF LAND. CHAP. III. 

v 

. , 1 • ’■ ■. .-"4 

’ 1 ) . • • - ■ , "* ■ i , ' * ‘ ' 

EXAMPLES. 

1. Required the area of a triangular tract of land, 
whose three sides are 49.00, £0.25 and 25.69 chains. 


semiperimeter of the triangle ABC. But since twice AD, twice BD, 
and twice CF are the sum of the sides of the triangle, or twice AH, 
it is obvious that AD, BD and CF together, are equal to AH ; conse¬ 
quently CF is equal to BH or BM ; hence CM or CL is equal to BF 
or BD ; and therefore DH and BC are equal. 

If now from the semiperimenter AH, the three sides AB, AC and 
BC be severally taken, the remainders will be BH, CL, (or BD) and 
AD respectively. 

Again, since the angles DBF and DGF are together equal to two 
right angles, as likewise DBF and FBH together equal to two 
right angles, it is manifest that the angle DGF is equal to the angle 
HBF ; and the angle DGB to the angle HBK ; the triangles DBG 
and HKB are therefore similar. Hence BD : DG : : KH : HB ; 
also in the similar triangles ADG, AHK, AD : DG : : AH : HK ; 
therefore (C.6) AD x BD : DG 2 : :AH: HB : : AH 2 : AH X HB. 

If therefore we take between AD and BD, and between AH and 
HB, the mean proportionals M and N respectively, the foregoing an¬ 
alogy will become M 2 : DG 2 :: AH 2 : N 2 ; hence (22.6) M : DG : : 
AH : N ; consequently the rectangle M X N is equal to the rectangle 
AII x DG ; therefore ABC=ABG+BCG+ACG=AH X DG=M x 
N=V (AD x BD) x \/ (AH x HB) = yf (AB x BD x HB x AH.) 






CHAP. III. 


CONTENT OP LAND. 


129 



49.00 

, \ ' 

. ■■ • * 

• ■ . / 


50.25 

• 

• 

25.69 

' ‘ l - 

Sum 

124.94 

r * 

- - 4 ^ ^ f 

V / y/sBl ‘ * 

Half sum 

62.47 

log. 1.79567 

^ j 

C 13.47 . 

1.12937 

Remainders 

1 12.22 

1.08707 

\ 

( 36.78 

1.56561 



2)5.57772 

> 

« ‘ . '; '' 

615 chains 

2.78886 


61.5 Acres—61 A. 2 R. 

2. What is the area of a triangular field whose sides 
measure 10.64, 12.28 and 9.00 chains ? 

Ans. 4 A. 2 R. 26 P. 

3. What quantity of land is contained in a triangle, the 
sides of which are 20, 30 and 40 chains ? 

Ans. 29 A. 0 R. 7 P. 

, \ . s , . i • 

PROBLEM VI. 

To find the area of a trapezium,' when one of the diagonals 
and the two perpendiculars let fall on it from the opposite 
angles, are given . 


RULE. 

Multiply the sum of the perpendiculars by the diago¬ 
nal, and half the product will be the area.* 


* Demonstration. The area of the triangle ABC= 


ACxBF 

2 


AC x DE 

and the area of the triangle ADC=- - -; therefore the sum 


R 


2 










130 


CONTENT OF LAND. 


CHAP. Ill 


JYote. When all .the sides and one of the diagonals 
are given, the trapezium will be divided into two trian¬ 
gles, the area of each of which may be found by the last 
problem. The sum of these areas will be the area of 
the trapezium. 

V 'ft- £ 1 \ 

r ‘ " . • 1 

EXAMPLES. 

_ 

1. In a field ABCD in the form of a trapezium, the 
diagonal AC measures 20.64 chains, the perpendicular 
BF 6.96 chains, and DE 5.92 chains ; required the area. 
Fig. 70. 

Ch. 

6.96 

5.92 


12.88 

20.64 


5152 

7728 

2576 
__ 

2)265.8432 . '• 

132.9216 Ch.= 13 A. 1 R. 6 P. 

if f* A 

2. Required the area of a trapezium whose diagonal 

measures 16.10 ch. and the perpendiculars 6.80 ch. and 
3.40 ch. Am. 8 A. 0 R. 33| P. 

• f 

3. The diagonal of a trapezium is 24 ch. and the per¬ 

pendiculars are 8.27 ch., and 12.43 ch.; what is the 
area ? Arts 24 A 3 R. 14 P. 


of these areas, or the area of the trapezium ABCD=---{■ 

ACxDE BF-J-DE 

XAC. Fig. 70. ^ 


2 


2 










CHAP. III. 


CONTENT OP LAND. 


131 


PROBLEM VII. 

To find the area of a trapezium , when all the angles and two 

opposite sides are given. 

Note. When three of the angles are given , the fourth may 
be found by subtracting their sum from 360°. 

RULE. 

. * - i* * . > * 

Consider one of the given sides and its adjacent an¬ 
gles, or their supplements when their sum exceeds 180°, 
as the side and adjacent angles of a triangle, and find its 
double area by prob. 4. Proceed in the same manner 
with the other given side and its adjacent angles: Half 
the difference of the areas thus found will be the area of 
the trapezium.* 

EXAMPLES. 

L In a four-sided field ABCD, there are given the 
following bearings and distances, viz. AB, N. 24° E. 
dist. 6.90 ch. BC, N. 64° 40' E. CD, S. 35° 20' E. dist. 
11.50 ch. and DA, S. 88° W.: required the area. Fig. 

71. 

From the given bearings, the angles may be found as 
follows: 

AD, N. 88° E. CB, S. 64° 40' W, 

AB, N. 24 E. CD, S. 35 20 E. 

BAD=64° BCD=100° 00 


* Demonstration. Let AB, CD, Fig. 71, be the given sides of 
the trapezium ABCD. Produce DA, CB, to meet in E, then 2 


ABCD=2 EDC—2 EAB or ABCD = 


2 EDC—2 EAB. 


Hence the 


truth of the rule is evident. 


2 






132 


CONTENT OF LAND. 


CHAP, in* 


BC, N. 64° 40' E. DC, N. 35° 20' W. 
BA, S. 24 00 W. DA, S. 88 00 W. 


40 40 
180 00 


ABC=139 20 


123 20 
180 00 


ADC = 56 40 


Construction. 


Make AB=6.90, and draw DA, CB, making the 
angle DAB=64°, and ABC =139° 20'; produce DA 
and make the angle EAF=56° 40'=the given angle 
ADC; lay off AF = 11.50=the given side BD, and pa¬ 
rallel to AD draw FC, meeting BC in C; lastly draw 
CD parallel to AF, meeting AD in D, then will ABCD 
be the trapezium.* 

Calculation. 


The angle E=180°—the sum of the angles BCD, 
ADC=23° 20'. 


As rad. x sin. E. 

: sin. EAB x sin. EBA, 
: : AB% 


( rad. Ar. Co. 0.00000 

\ sin. E 23°20' Ar. Co. 0.40222 
( sin. EAB 116° 00' 9.95366 

I sin. EBA 40 40 9.81402 

( AB 6.90 0.83885 

}AB 6.90 0.83885 


: 2 EAB 70.405 


1.84760 


* Demonstration. By construction FC is parallel to AD and CD 
to AF, therefore (34.1.) CD=AF and (29.1.) the angle ADC 
=EAF ; hence it is evident that the sides AB, CD, and the angles 
of the trapezium ABCD are respectively equal to the given sides and 
angles. 








CHAP. III. 


CONTENT OP LAND. 


133 


As rad. x sin. E, 

: sin. ECD X sin. EDC, 
: : CD 2 

\ 


S rad. Ar. Co. 0.00000 

{ sin. E. 23° 20' Ar. Co. 0.40222 
X sin. ECD 100° 00' 9.99335 
\ sin. EDC 56 40 9.92194 

X CD 11.50 1.06070 

l CD n.50 1.06070 


: 2 EDC 274.731 2.43891 

2 EAB 70.405 


2 ABCD 204.326 

ABCD =102.163 Ch. = 10 A. 0 R. 34.6 P. 

2. In a trapezium ABCD, the angles are, A=65° B 
= 81°, C=120°, and consequently D=94°; also the 
side AB=20 ch. and CD=11 ch.: required the area. 

Ans. 22 A. 2 R. 27 P. 


3. Required the area of a four-sided piece of land, 
bounded as follows: 

1. N. 12° 30' E. 

2. N. 81 00 E. dist. 23.20 ch. 

3. S. 36 00 W. 

4. N. 89 00 W. dist. 12.90 ch. 

Ans . 27 A. 2 R. 24 P. 


PROBLEM VIII. 

To find the area of a trapezium when three sides and the 
tivo included angles are given. 

RULE. 

As radius, 

Is to the sine of one of the given angles; 

So is the rectangle of the sides including this angle, 
To a certain quantity. 




CHAP. III. 


134 CONTENT OF LAND. 

As radius, 

Is to the sine of the other given angle; 

So is the rectangle of the sides including this other 
angle, 

To a second quantity. 

i * ' 

Take the difference between the sum of the given an¬ 
gles and 180 ° ; Then, 

As radius, 

Is to the sine of this difference; 

So is the rectangle of the opposite given sides, 

To a third quantity. 

- \ -• / mBS S 

* '■ \ 

If the sum of the angles be less than 180 °, subtract 
the third quantity from the sum of the other two, and 
half the difference will be the area of the trapezium. 
But if the sum of the given angles exceed 180°, add all 
the three quantities together and half the sum will be 
the area. # 


* Demonstration. Let ABCD (Fig. 72 or 73) be the trapezium, 
having the given sides, AD, AB, BC, and given angles DAB, ABC. 
Complete the parallelograms ABCE, ABFD, and join ED ,CF ; then 
because EC, DF, are each parallel and equal to AB, they are (30.1.) 
parallel and equal to each other, and (33.1.) ECFD is a parallelo¬ 
gram ; therefore ABFD = ABIIG -f-GHFD = (35.1.) ABCE-f- 
ECFD—(34.1.) ABCE-f-2 ECD ; to the first and last of these equals 
add ABCE, then ABFD-{-ABCE=2 ABCE+2 ECD=2 ABCDE. 

But, Fig. 72, when the sum of the given angles DAB, ABC, is less 
than 180°, 2 ABCDE=2 ABCD-f-2 EAD ; therefore in this case 
ABFD+ABCE=2 ABCD+2 EAD ; or ABFD-f-ABCE—2 EAD 
= 2 ABCD. 

/ '/"* •. » :kaiJ fr« 

\ V- 

And, Fig. 73, when the sum of the given angles DAB, ABC, ex¬ 
ceeds 180°, 2 ABCDE=2 ABCD—2 EAD ; therefore ABFD+ 
ABCE=2 ABCD—2 EAD ; or, ABFD+ABCE+2 EAD=2 
ABCD. 





CHAP. III. 


CONTENT OP LAND. 


135 


EXAMPLES. 

1. Tn a trapezium ABCD, there are given AD— 
23.32 ch. AB.=25.70 ch., and BC=15.84 ch., the an- 
gle DAB=64° and ABC=82°: required the area. 


As rad. ... 

: sin. DAB, 64° 

• . ADvAD S AD 23.32 

• ' AUxAB >J ab25.70 

: first quantity 538.66 

As rad. - 
: sin. ABC, 82° 

• AByRC 5 AB 25.70 

.. AiixBO, f BC 15g4 

: second quantity 403.12 

DAB 64° 
ABC 82 


146 

180 


Difference 34° 


As rad. - 

: sin. difference 34° - 

AD 23.32- 
BC 15.84 - 


:: ADxBC 


• s 


third quantity 206.65 


Ar Co. 0.00000 
9.95366 

1.36773 

1.40993 


2.73132 


Ar. Co. 0.00000 
9.99575 

1.40993 

1.19975 


2.60543 


Ar. Co. 0.00000 
9.74756 

1.36773 

1.19975 


2.31504 


But by prob. 3. one of the first two proportions gives 2 BAD 
(=ABFD,) and the other gives 2 ABC (—ABCE ;) also because 
angle EAD is the difference between the sum of the given angles and 
180°, and the side EA=BC, the third proportion gives 2 EAD : hence 
the truth of the rule is manifest. 








136 


CHAP. III. 


CONTENT OF LAND. 

• \ 

1st quantity 538.66 
2nd — 403.12 


941.78 
3rd 206.55 

yv \ , 2)735.23 

- 

367.615 Ch.=36 A. 3 R. 2 P. 

2. What is the area of a four-sided lot of ground, 
three sides of which, taken in order, measure 6.15,8.46 
and 7.00 chains, respectively, the angle contained by 
the first and second sides 56°, and that contained by 
the second and third sides 98° 30' ? 

Ans. 4 A. 0 R. 25 P. 

3. One side of a quadrilateral piece of land bears S. 7 i 

E. dist. 17.53 ch., the second, N. 87 E. dist. 10. 80 ch. 
and the third, N. 251 E. dist. 12.92 ch.: what is the 
area? Ans. 21 A. 3 R. 2 P. 

PROBLEM IX. 

To find the area of a trapezoid. 

• N ,i • 

RULE. 

Multiply the sum of the parallel sides by their per¬ 
pendicular distance, and half the product will be the 
area.* 

EXAMPLES. 

1. Required the area of a trapezoid ABCD, of which 
the parallel sides AD, BC measure 6.14 and 9.48 chains. 


* Demonstration. The trapezoid ABCD, Fig. 74,—the triangle 
ABD+BDC=(by prob. 2,) ADxBF+5^2^. _(becauseBF= 

ADxBF BCxBF AD+BCxBF. 

0 <? ~r Q — 


2 


2 













CHAP. HI. 


CONTENT OF LAND. 


137 


respectively, and their perpendicular distance BF or 
DE, 7.80 chains. 

* , ' • V. ■ / 

Ch. 

6.14 

9.48 


15.62 

7.80 


124960 

10934 

2)121.8360 


60.9180 Ch.=r6 A. OR. 15 P. 

2. The parallel sides of a trapezoid are 12.41 and 
8.22 chains, and their perpendicular distance 5.15 
chains: required the area. Ans. 5 A. 1 R. 10 P. 

* < » ^ ,v' , ,< 

3. Required the area of a trapezoid whose parallel 
sides are 11.34 and 18.46 chains, and their perpendi¬ 
cular distance 13.25 chains. Ans. 19 A. 2 R. 39 P. 

PROBLEM X. 

To find the area of a circle , or of an ellipsis* 

■ . ~' n ‘ ' / \ . u v , 

RULE. 

Multiply the square of the circle’s diameter, or the 


* If two pins be set upright in a plane, and a thread, the length of 
which is greater than twice the distance between the pins, having the 
ends tied together, be put about the pins ; and if the point of a pin or 
pencil, applied to the thread, and held so as to keep it uniformly tense, 
be moved round, till it return to the place from which the motion be¬ 
gan ; then the point of the pin or pencil will have described on the 

plane, a curved line called an j Ellipsis. 

S 







138 


CONTENT OF LAND. 


chap, in- 


product of the two diameters of the ellipsis, by .7 854, 
for the area.* 

Note 1. If the diameter of a circle be multiplied by 
3.1416, the product will be the circumference; also if 
the circumference be divided by 3.1416, the quotient 
will be the diameter. 

2. If the area of a circle- be divided by .7854, the 

square root of the quotient will be the diameter. 

r , • >. , ~ f 

- % , r 

EXAMPLES. 

1. How many acres are in a circle a mile in diameter? 

1. mile=80 ch. 

80 

6400 , 

.7854 

3141600 

47124 

5026.5600 Sq. Ch.=502 A. 2 R. 25 P. nearly. 

Or by Logarithms. 

Square of 80 j ^ 

.7854 

5026.56 Sq. Ch. 

2. Required the area of an ellipsis, the longer diame¬ 
ter of which measures 5.36 ch. and the shorter 3.28 ch. 


* The demonstration of this rule is too abstruse to admit of a place 
in this work. The student who wishes to see a demonstration is re¬ 
ferred to treatise on Mensuration or Fluxions. 


log. 1.90309 
1.90309 
—1.89509 


3.70127 

4 







CHAP. III. 


CONTENT OP LAND. 


139 


Ch. 

5.36 

3.28 


4288 

1072 

1608 


17.5808 

.7854 


703232 

879040 

1406464 

1230656 


13.80796032 Sq. Ch.= 1 A. 1 R. 20.9 P. 


PROBLEM XI. 

The bearings and distances of the sides of a tract of land 
being given , to calculate the area. 

RULE. 

1. Rule a ta$le and head it as in the annexed example; 
observing that the letters E. D. D. and W. D. D.. stand 

for East Double Departure , and West Double Departure. 

2. Find by prob. 12. chap. 1., the corrected differ¬ 
ences of latitude and the departures, corresponding to 
the several sides, placing them in their proper places in 
the table. 

3. When the departures corresponding to the first and 
last sides are of the same name, add them together, and 
place the sum opposite the first side, in the column of 
double departures, which is of that name; but when they 
are of different names, take their difference , and place it 






140 


CONTENT OF LAND. 


CHAP. III. 


in the column of double departures, which is of the same 
name with the greater departure. Proceed in the same 
manner with the departures corresponding to the first 
and second sides, placing the result opposite the second 
side; with those corresponding to the second and third 
sides, placing the result opposite the third side; and so 
on to the last. 

4. Commencing with any side of the survey at plea¬ 
sure, assume any number whatever for a multiplier cor¬ 
responding to that side, and place it in the column of 
multipliers, opposite to the side, marking it with the 
letter E, for east. If this multiplier and the double de¬ 
parture, corresponding to the next side, are of the same 
name, take their sum for the next multiplier, marking it 
with that name; but if they are of different names, take 
their difference, marking it with the name of the greater. 
Proceed in the same way with this multiplier and the 
next double departure; and so on till multipliers have 
been found corresponding to all the sides. 

5. Multiply each of the corrected differences of lati¬ 
tude by its corresponding multiplier; and when the 
multiplier is east , place the product in that column of 
areas, which is of the same name with the difference of 
latitude; but when it is ivcst , place the product in the 
column of areas, which is of a different name from that 
of the difference of latitude. 

6. Add up the numbers in the columns of areas, and 
taking the difference of their sums, divide it by 2; the 
result will be the area of the survey.* 


* Demonstration. Let ABCDEFG, Fig. 79, be a plot of survey ; 
and let the east and west line AL, represent the assumed multiplier. 
From the points B and L, draw BM parallel, and LM perpendi- 



CHAP. III. 


CONTENT OF LAND. 


141 


Note 1. The sums of the two columns of double de¬ 
partures, will, if these have been correctly found, be 
equal. Also, if the multipliers have been correctly ob- 


cular to AL, meeting in M ; and bisect BM by the meridian NS. 
Draw the other east and west lines, Cc, md, ne, rf, and ug; and also the 
meridians hk, Bp, Cn , Ds, ur , Fw , and Gx. Then it is evident that 
the differences of latitude and the departures corresponding to the 
several sides will be as in the following table. Also that according to 


the rule, Bh-{- Av—Bx, is the double departure corresponding to the 
first side ; Bh-\-01= Ck, is that for the second side ; Cl — Dm=Dp , 
is that for the third, and so on to the last. 


Dist. 

N. 

S.l 

E. 

W. 

E.l>7D. 

WDD. 

Multipliers. 

N. Areas. 

S. Areas. 

AB 

Ah 


Bh 


Bx 


Aa-\~Bb, 

E 

2 Aab B 


BC 


Bl 

Cl 


Ck 


Bb+Cc, 

E 


2. BbcC 

CD 


Cm 


Dm 

Dp 


Cc+Dd, 

E 


2. CcdD 

DE 


Dq 

Eq 



En 

Dd-\~Ee, 

E 


2. DdeE 

EF 


Er 


Fr 


Fs 

Ee+Ff, 

E 


2. EefF 

FG 

Ft 



Gt 


Gu 

F/+ Gg, 

E 

I.Ffg G 


GA 

Gv 


Av 


Aw 


Gg-j-Aa, E 

2 Gga A 



By construction, the assumed multiplier AL=Aa+aL=Aa+bM 
=Aa+Bb. By proceeding with this multiplier and the double 
departures, as directed in the rule, we shall evidently have the other 
multipliers as represented in the table. It is also plain that the 
products of the differences of latitude by these multipliers will be as 
represented in the columns of north and south areas. 

The sum of the north areas is 2. BAGFfbB; and the sum of 
the south areas is 2. BCDEFfbB. The difference of these is 2. 
ABCDEFGA ; the half of which is the area of the survey. 


The preceding demonstration may easily be extended to the 















































































142 


CONTENT OF LAND. 


CHAP. III. 


tained, the sum or difference of the multiplier last 
found and the next double departure, according as they 
are of the same or different names, will be equal to the 

, i « 

assumed multiplier. 

2. It is best, in general, to assume 0, for the first 
multiplier; as by so doing there is one multiplication 
less to be performed, and the other multipliers are 
mostly smaller numbers, than they would otherwise be. 


case in which the assumed multiplier is so small as to make the meri¬ 
dian NS pass through the survey. Thus, suppose Aw+HB to be the 
assumed multiplier, the meridian in this case coinciding with FH. 
Then the multipliers will be equal to the difleiences between the 
above multipliers and the quantity, wa-fbH, or its equal 2.bH. We 
may therefore represent them, and the products as in the following 
table ; in which the multipliers are marked, and the products placed, 
in conformity with the rule. 


Dist. 

N. 

s. 

Multipliers. 

N. Areas. 

S. Areas. 

AB 

Ah 


(Aa+Bb)—2.bH, E. 

2AaBb —2 .wabH 


BC 


Bl 

(Bb+Cc)—2.bH, E. 


Q.BbcC — 2HbcK 

CD 


Cm 

(Cc+Dd)—2.bH, E. 


Q.CcdD — Q.KcdP 

DE 


Dq 

{Dd+Ec)—2.bH, E. 


Z.DdeE — 2PdeQ 

EF 


Er 

(Ee+Ff)—2.bH, E. 


2. EcfF—2.QefF 

FG 

Ft 


2.bH— (If+Gg,)W. 


2.Ffgt-2.FfgG 

GA 

Gv 


2.bH— (Gg+A«,)W. 


2.tgaw — 2 .GgaA 


The sum of the north areas is 2.AabB—2.Hbaw : and the sum of 
the south areas is 2. BCDEFfbB+2.waf F— 2. HbfF—2.AGFfa 
=2.BCDEFf bB + 2.waf F.—2.waf F.—2.Hbaw — 2.AGFfa = 
2.BCDEFfbB—2.IIbaw— 2.AGFfa=2.BCDEFf bB — 2.AGFfa.~ 
2.Hbaw. If now the sum of the north areas be subtracted from that of 
the south areas, the remainder will be 2.BCDEFf bB—2.AGFfa— 
2.AabB=2.BCDEFfbB—2.BAGFfb=2.ABCDEFGA. 











































CHAP. III. 


CONTENT OF LAND. 


143 


3. Instead of assuming the first multiplier east, it 
might with equal propriety be assumed west . Also 
instead of finding the multipliers from the departures, 
they might be found in a similar manner, from the dif¬ 
ferences of latitude, using in that case the departures 
for multiplicands. 

4. When one or two bearings or distances are 
omitted, they may be found by the problems in the last 
chapter; and in these cases the differences of latitude 
and departures are to be used as first obtained from the 

tables, there being no means of correcting them. 

% 

EXAMPLES. 

1. Given the bearings and distances of the sides of a 
tract of land as follow: 1st. 40£° E. 31.80 ch.; 2nd. N. 
54° E. 2.08 ch.; 3rd. N. 29*° E. 2.21 ch.; 4th. N. 28f° 
E. 35.35 ch.; 5th. N. 57° W. 21.10 ch.; and 6th. S. 47° 
W. 31.30 ch. to the place of beginning. Required the 
area of the tract. 


144 


CONTENT OF LAND 


CHAP. Ill 


S. Areas. 






45.9455 

45.9455 

5 

95 

4 

20 

40 

300 

N. Areas. 

i 

27.5274 

48.2688 

1339.6392 

489.3102 


1904.7456 

45.9455 

) 1858.8001 

0)929.4000, 

92.94001 

3.7600! 

30.4001 

Multipli¬ 

ers. 

0.00 E 

22.38 E 

25.14 E 

43.27 E 

42.66 E 

W 

© 

T—» 

c* 

©* 

iW.D.D. 

2.15 



* 

I9'0 

40.51 

43.27 

E.D.D 


CO 

CO 

©* 

2.76 

18.13 



| 43.27 

W. 





© 

CO 

t- 

r-H 

to 

© 

©$ 

©* 

40.51 | 

W 

20.70 

1.68 

CO 

© 

T-H 

17.05 



T-. 

© 

© 

xn 

©* 

©* 

• 




21.37 

© 

© ‘ • 

© rtj 



1.23 

1.92 

30.96 

11.47 


45.58 

3R.30 

Cor 

E. 

.05 

.00 

.00 

.05 

.03 

.04 

t-h rj ^ 

* 

Cor 

S. 

.03 

o 

© 

© 

© 

.04 

.02 

.03 

Gs* »-. © 

r! W «a 

C3 

w. 





© 

CO 

r—< 

22.89 

40.58 

40.41 

.17 

An 


( 20.65 

89‘1 

SOT 

© 

© 



40.41 

02 

24.18 





21.34 

©* Xfl 

© w 

© *- 

^ w 

• 

£ 


1.23 

1.92 

31.00 

11.49 


Tt< ©* ©* 

© © 

4 « • • 
to © 

• 

U1 

Q 

31.30 

2.08 

IZ'Z 

35.35 

© 

t-H 

• 

1.30 

© 

c© 

©* 

T"H 

Bearings. 

H 

o 

02 

N. 54 E. 

w 

©* 

• 

{25 

H 

© 

©< 

• 

£ 

N. 57. W. 

S. 47 W. 


Sta 

rH 

©* 

CO 

* 

© 

© 



2. Required the area of a tract of land, bounded as 
follows: 1st. N. 75° E. 13.70 ch.; 2nd. N. 20*° E. 10.30 
ch.; 3rd. East, 16.20 ch.; 4th. S. 334° W. 35.30 ch.; 
5th. S. 76° W. 16 ch.; 6th. North, 9 ch.; 7th. S. 84° 




















































































































CHAP. IH 


CONTENT OF LAND 


145 


W. 11.60 ch.; 8th. N. 53i° W. 11.60 ch.; 9th. N. 36|° 
E. 19.36 ch.; 10th. N. 22i° E. 14 ch.; 11th. S. 76|° E. 
12 ch.; 12th. S. 15°'W. 10.85 ch.; 13th. S. 18° W. 10.62 
ch.; to the place of beginning. 















































































































































































































































146 CONTENT OF LAND. CHAP. 111. 

3. Given the boundaries of a tract of land as follow, 

viz. 1st. S. 35i° W. 11.20 ch.; 2nd. N. 45° W. 24.36 ch. 
3rd. N. 15|° E. 10.80 ch. 4th. S. 77° E. 16. ch. 5th. N. 
87 a° E. 21.50 ch. 6th. S. 60 3 E. 14.80 ch. South 10.91 
ch. 8th. N. 85° W. 29.28 ch. to the place of beginning: 
required the area. Ans. 85 A. 3 R. 17 P. 

4. Given the boundaries of a tract of land as follow, 
viz. 1st. N. 19° E. 27 ch. 2nd. S. 77° E. 22.75 ch. 3rd. 

S. 27° E. 28.75 ch. 4th. S. 52° W. 14.50 ch. 5th. S. 15£° 
E. 19 ch. 6th. West, 17.72 ch. 7th. N. 36° W. 11.75 ch. 
8th. North, 16.07 ch. 9th. N. 62° W. 14.88 ch. to the 
place of beginning : required the area. 

Ans . 152 A. 2 R. 6 P. 

5. Required the area of a tract of land bounded as 
follows : 1st. S. 62° W. 7.57 ch. 2nd. N. 432° W. 5.89 ch. 
3rd. North, 5.82 ch. 4th. N. 33£° W. 8.83 ch. 5th. N. 
48° E. 4.81 ch. 6th. N. 12° E. 4.66 ch. 7th. N. 62£° E. 
5.27 ch. 8th. S. 6i° E. 5.60 ch. 9th. S. 40F E. 5.87 ch. 
10th. East, 6.54 ch. lltli. North, 5.52 ch. 12th. N. 68£° 
E. 3.10 ch. 13th. S. 30° E. 7.90 ch. 14th. S. 23° W. 8.80 
ch. 15th. S. 3H° E. 6.42 ch. 16th. S.'50° W. 8.40 ch. 
17th. N. 44° W. 6.85 ch. to the place of beginning. 

Ans . 44 A. 2 R. 18 P. 

6. Given the following field-notes to find the area of 
the survey; also the bearings and distance of the 3rd 
side, which were omitted to be taken on account of 
obstacles in the way. 

Ch. 

1. S. 851° E. 23.30 

2. S. 19 E. 31.12 

3. -- - 

4. N. 64 W. 29.72 




CHAP. HI. 


CONTENT OF LAND. 


147 


Ch. 



7. S. 27! E. 6.G0 

Ans. Area 182 A. OR. 21.7 P. and the bearing and 
distance of the 3rd side, S. 66° 23' W. 28.06 ch. 

7. Being furnished with the field-notes of a tract of 
land, and requested to calculate the area, I found on 
examining them, that the figures expressing the angles 
of bearing of the 4th and 5th sides were so defaced as 
to be illegible : but as the remaining data are sufficient, 
the area is required. The field-notes are as follow. 


Ch. 


1. S. 603° W. 10.34 

2. N. 27! W. 17.88 

3. N. 51 E. 15.85 

4. N. — E. 9.61 

5. S. — E. 19.18 

6. S. 16f E. 22.21 

7. S. 71! W. 16.66 

8. N. 71 £ W. 5.56 




2 R. 27 F. 


Ans. 81 A 


8. In a survey, represented Fig. 81, the corner at A 
was inaccessible, occasioned by the overflowing ol 
water, but being a tree, it can be seen from the adja¬ 
cent corners B and L. I therefore set my instrument 
at B and took the bearing to A, which I reversed, and 
set my field-book as the first bearing. I then proceeded 
to take the bearings and distances of the several sides 
to L; and at L, I took the bearing of the side LA. The 
field-notes being as follow, the length of the sides AB 
and LA, and the area are required. 






148 CONTENT OF LAND. CHAP. III. 

Ch. 

AB, N. 51i° W. 

BC, S. 454 W. 15.16 

CD, N. 50 W. 22.10 

DE, North 18.83 

EF, N. 48 E. 22.60 ' . ‘ 

FG,N. 254 W. 20.17 

GH, East 26.57 

HI, S. 304 E. 22.86 

, IK, S. 44 W. 15.04 • 

KL, S. 47 E. 28.55 
LA, S.20J W. 

,/his. AB 26.47 ch.; LA 23.80 ch.; and the 

area 244 A. 3 R. 13 P. 

% 

9. In taking a survey of a tract of land bounded by 
six straight sides, (Fig. 80,) I was prevented going di¬ 
rectly from the 3rd to the 4th corner by a pond of 
water. I therefore set up two stakes near the edge 
of the pond, and took the bearing and distance from 
the 3rd corner to the first stake, from the first stake to 
the second, and from the second to the 4th corner, and 
noted them in my field book as all belonging to the 3rd 
station of the survey. The field-notes being as follow, 
the bearing and distance the 3rd side, and the area of 
the survey are required. 

Ch. 

1. North 7.81 

2. S. 76i° E. 18.15 

C S. 52 W. 10.70 ) 

3. {S. 7i W. 13.92 > 

!> . v ( S. 33* E. 9.00) 

4. N. 84* W. 27.12 

5. N. 41 W. 22.00 

6. East, 16.58 

Ans. 3rd side, S. 10° 47' W. 28.42 ch.; and 
area 80 A. 0 R. 25 P. 


\ 




CHAP. III. 


CONTENT OF LAND. 


149 


PROBLEM XII. 

To find area when off-sets are taken. 

RULE. 

1. Find by the last problem, the area enclosed by 
the stationary lines and straight sides of the survey. 

2. Subtract the stationary distance of each off-set, 
from that of the one immediately following; the re¬ 
mainders will be the distances, intercepted on the sta¬ 
tionary line, between each two adjacent off-sets. 
Place these under one another in a column as in the 

* j . > , * * 

annexed examples. Also take the sums of each two 
adjacent off-sets, and place them in the next column, 
so as to correspond with the intercepted distances. 

3. Multiply the sum of each two adjacent off-sets by 
their intercepted distance on the stationary line; then, 
half the sum of the products will be the area of the off¬ 
sets on that line. 

4. If there are off-sets on more than one stationary 
line, proceed in the same manner with the others. 

5. When the stationary lines are within the boun¬ 
dary of the survey, add the areas of the off-sets to the 
area enclosed by the stationary lines and straight sides; 
but when the stationary lines are without the boundary, 
subtract the areas of the off-sets.* 


* Demonstration. Considering the boundary as straight between 
the ends of each two adjacent off-sets, it is plain that the area con¬ 
tained between the stationary line and boundary will be divided by 
the off-sets into trapezoides and triangles. Hence the truth of the 
rule is evident. 




I 


% 




150 CONTENT OF LAND. CHAP. III. 

Example 1 . Fig. 82. 

* 

Required the area of a piece of a meadow, bounded 
on one side by a brook, the field notes being as follow. 

Left-hand off-sets on the stat. line. 




Sta. 

Dist. 

Off-sets. 


Ch. 

No. 

Ch. 

Ch. 

1. N. 

16£° E. 14.35 

1. 

0.00 

0.30 

2. 

East, 7.82 

2. 

0.95 

0.84 

3. S. 

3h W. 14.45 Stat. line. 3. 

2.03 

0.86 

4. N. 

86 i W. 11.07 

4. 

3.28 

0.50 


. > , " j 

5. 

5.20 

1.80 


. 

6. 

7.43 

2.35 


* 

7. 

8.98 

1.45 



8. 

10.46 

1.08 



9. 

11.71 

1.85 



10. 

14.45 

0.35 

The area of the part ABCD 

will be 

found, 

by the 


last problem, to be 13 A. 1 R . 11 P. 


( 



CHAP. III. CONTENT OF LAND. J51 

To find the area of the off-sets. 


No. 

• 

Sta. Dist. 
Ch. 

Off-sets. 

Ch. 

Intercep. 

Dist. 

Sums of 
Off-sets. 

Products. 

1 

0.00 

0.30 



• • \ . ' ' 

2 

0.95 

0.84 

0.95 

1.14 

1.0830 

3 

2.03 

0.86 

1.08 

1.70 

1.8360 

4 

3.28 

0.50 

1.25 

1.36 

1.7000 

5 

5.20 

1.80 

1.92 

2.30 

4.4160 

6 

7.43 

2.35 

2.23 

4.15 

9.2545 

7 

8.98 

1.45 

1.55 

3.80 

5.8900 

8 

10.46 

1.08 

1.48 

2.53 

3.7444 

9 

11.71 

1.85 

1.25 

2.93 

3.6625 

10 

14.45 

0.35 

2.74 

2.20 

6.0280 


2)37.6144 


18.8072 Ch. 
= 1 A. 3 R. 21 R 

A. R. P. 

Area of ABCD 13 1 11 

Do. of off-sets 1 3 21 


Whole area 15 0 32 

Example 2. Fig. 83. 

i i 

Required the area of a survey from the following 
field-notes. 






































































152 


CONTENT OB 1 LAND. 


CHAP. III. 


Left hand off-sets. 

1st Stationary Line. 3rd Stat. Line. 
Sta. Dist. Off-sets. Sta. Dist. Off-sets. 




Ch. 


No. 

Ch. 

Ch. 

No. 

Ch. 

Ch. 

1. N. 36£° 

W. 

30.00 


1. 

0.00 

0.50 

1 . 

0.00 

0.55 

2. N. 56£ 

E. 

21.60 stat. line. 

2. 

6.10 

3.40 

2. 

4.20 

2.50 

vL. N. 26£ 

E. 

13.44 

Do. 

3. 

10.15 

3.10 

3. 

8.05 

3.20 

4. S. 7l£ 

E. 

18.96 

Do. 

4. 

14.08 

3.96 

4. 

15.15 

2.45 

5. S. 26£ 

E. 

13.46 

Do. 

5. 

19.20 

2.70 

5. 

18.96 

0.50 

6. S. 45 

W. 

42.41 


6. 

21.60 

0.55 

4th Stat. 

Line. 





2nd Stat. Line. 

1 . 

0.00 

0.50 

1 




1. 

0.00 

0.55 

2. 

5.12 

2.75 





2. 

13.44 

0.55 

3. 

10.00 

1.90 




m 




4. 

13.46 

0.70 


The area within the stationary lines and straight sides, 
found by the last problem, is 1152.5381 square chains. 

To find the area of the ojf-sets. 

1st Stationary Line. 


No. 

Sta. Dist. 
Ch. 

Off-sets. 

Ch. 

Intercep. 

Dist. 

Sums of 
Off-sets. 

Products. 

1 

0.00 

0.50 




2 

6.10 

3.40 

6.10 

3.90 

23.7900 

3 

10.15 

3.10 

4.05 

6.50 

26.3250 

4 

14.08 

3.96 

3.93 

7.06 

27.7458 

5 

19.20 

2.70 

5.12 

6.66 

34.0992 

6 

21.60 

0.55 

2.40 

3.25 

7.8000 


2nd Stationary Line. 


No. 

Sta. Dist. 
Ch. 

Off-sets. 

Ch. 

Intercep. 

Dist. 

Sums of 
Off-sets. 

Products. 

1 

0.00 

0.55 




2 

13.41 

0.55 

13.44 

1.10 

14.7840 




























































CHAP. III. 


CONTENT OF LAND. 
3rd Stationary line. 


153 


No. 

Sta. Dist. 
Ch. 

Off-sets. 

Ch. 

Intercep. 

Dist. 

i 

Sums of 
Off-sets. 

Products. 

1 

0.00 

0.55 




2 

4.20 

2.50 

4.20 

3.05 

12.8100 

3 

8.05 

3.20 

3.85 

5.70 

21.9450 

4 

15.15 

2.45 

7.10 

5.65 

40.1150 

5 

18.96 

0.50 

3.81 

2.95 

11.2395 

\ u 

0 

is' V 

$■ 

s , , 

4th Stationary line. 


• 

1 

0.00 

« 

0.5Q 




2 

5.12 

2.75 

5.12 

3.25 

16.6400 

3 

10.00 

1.90 

4.88 

4.65 

22.6920 

4 

13.46 

0.70 

3.46 

2.60 

8.9960 


U 


2)268.9815 




Area of the off-sets 

> . > • • • ; 1 ■ 1 i 

Area within the stationary linos 


144.39075 Ch. 
1152.5381 


1287.02885 Ch. 

128.702885 Acr. 
4 






2.811540 

40 


Area of the survey, 128 A. 2 R. 32 P. 
U 


32.46160 





























































154 CONTENT OF LAND. CHAP. III. 

EXAMPLE 3. 

Required the area of a meadow from the following 
field-notes. 

Left-hand off-sets on the stat. line. 






Sta. 

Dist. 

Off-sets. 


( 1 


Ch. 

No. 

Ch. 

Ch. 


l. 

N. 41i° 

E. 14.35 

1. 

0.00 

0.38 


2. 

S. 424 

E. 14.71 

stat. line. 2. 

2.65 

2.35 


3. 

S. 54 

W. 16.32 

3. 

3.80 

1.70 

jr 


W. 11.50 

4. 

6.00 

2.75 





5. 

7.50 

1.40 





6. 

9.60 

3.20 





7. 

12.38i 

2.72 



t ' 


8. 

14.71 

<5.42 




V 

Ans. Area 22 A- 3 R. 

27 P. 


\ \ * '. i 

EXAMPLE 4. 

The following field-notes are given to find the area 
of the survey. 

* 

Left-hand off-sets. 

s 

On the 1st stat. line. On the 2d stat. line. 
Sta. Dist. Off-sets. Sta. Dist. Off-sets. 
Ch. No. Ch. Ch. No. Ch. Ch. 

1. S. 69^° E. 16.14 stat. line 1. 0.00 0.44 1. 0.00 0.31 

2. S. 28 E. 9.38 Do. 

3. S. 321 W. 21.20 

4. N. 48 W. 22.47 

5. N. 26j E. 19.00^ . 

V. * 

% 

* *. 

.. 7 * r " 


2. 3.80 2.00 2. 2.67 2.94 

3. 7.04 3.79 3. 6.20 2.62 

4. 9.87 2.34 4. 9.38 0.39 

5. 13.24 3.00 

6. 16.14 0.31 

Ans. 56 A. 2 R. 19 P. 


I 



CHAP. III. 


CONTENT OF LAND. 


155 


/ ' , \ , t ) 

• 

PROBLEM XIII. 

Given the bearing and distance of two stations from each 
other , and the bearings of all the corners of a tract of 
land from these stations , to find the area of the tract. 

The method of doing this will be best explained by 
an example. 


example 1. 

Let ABCDEFGA, Fig. 84, represent a field, all the 
angles of which can be seen from two stations H and I 
without it. The bearing and distance of the stations, 
and the bearings of all the angles of the field, from each 
station, being as follow, it is required to find the area. 

The station H bears from the station I, North, dist. 
28 Ch. 



Bearings. 


Bearings. 

HA 

s. 

814° 

E. 

IA 

N. 284° 

E. 

HB 

s. 

CO 

E. 

IB 

N. 424 

E. 

HC 

s. 

68 

E. 

IC 

N. 514 

E. 

HD 

s. 

■- | H‘ 

CO 

E. 

ID 

N. 71 

E. 

HE 

s. 

3 5i 

E. 

IE 

S. 824 

E. 

HF 

s. 

284 

E. 

IF 

N. 734 

E. 

HG 

s. 

40 

E. 

IG 

N. 60 

E. 


Construction. 


Draw HI according to the given bearing and distance, 
and from ihe points Hand I, draw HA. HB, HC, fcc. 


































156 


CONTENT OF LAND. 


CHAP. III. 


and IA, IB, IC, &c. according to the given bearings; 
then will the intersections A, B, C, &c. of the corres¬ 
ponding bearings HA and IA, HB and IB, HC and IC, 
&c. be the angular points of the field. 

■ „ . \ f , \ N • * 

Calculation. 

In each of the triangles IHA, IHB, IHC, &c. we 
have the side IH, and from the bearings of the sides, we 
have all the angles, to find the sides IA, IB, IC, &c. 

Then in each of the triangles, IAB, IBC, ICD, &c. 
we have two sides and the included angle; whence the 
areas may be found by prob. III. 

From the sum of the areas of the triangles IAB, IBC, 
ICD, and IDE, which is equal to the area IABCDEI, 
subtract the sum of the areas of the triangles IAG, IGF 
and IFE, which is equal to the area IAGFEI, the re¬ 
mainder will be the area of the field ABCDEFGA. 

Note. In working the proportions for finding the sides 
IA, IB, &c. it will be unnecessary, when the area only 
is required, to take out the natural numbers correspond¬ 
ing to the logarithms of those sides; because in the pro¬ 
portions for finding the areas it will be sufficient to 
know the logarithms of the sides, without knowing 
their real lengths. 

To find the log. of IA. 

As sin. HAI70° 00' - - 9.97299 

: sin. AHI 81 30 - - 9.99520 

IH 28 - - - - 1.44716 

11.44236 



log. I 46937 




I 


1 

\ \ ' 

t 

CHAT*. III. CONTENT OF LAND. 157 


To find the log. of IB. 


As sin. HBI 52° 00' 
: sin. BHI 85 45 
: : IH 28 


9.89653 

9.99880 

1.44716 

, Jt ; 



11.44596 
log. 1.54943 

' 


To find the log. of IC. 

As sin. HCI 60° 30' - - - 9.93970 

: sin. CHI 68 00 - - - 9.96717 

:: IH 28 - - - - 1.44716 

• t 

* '* ■ • V 

- - - — r 

l | 

11.41433 


: 1C log. 1.4746.3 


To find the log. of ID. 

As sin. HDI 50° 45' - 
: sin. DHI 58 15 - 
:: IH 28. 


9.88896 

9.92960 

1.44716 


11.37676 


: ID log. 1.48780 

* i 

To find the log. of IE. 

As sin. HE! 47° 00' - - - 9.86413 

: sin. EHI 35 30 - - - 9.76395 

: : IH 28 - - - 1.44716 


11.21111 


log. 1.34698 


: IE 












158 










* A 

CONTENT OP LAND. 


CHAP.'III. 


To find the log. of IF. 

As sin. HFI 78° 00' - 
: sin. FHI 28 30 - 
: : IH 28 


9.99040 

9.67866 

1.44716 


11.12582 




log. 1.13542 


To find the log. of IG. 

As sin. HG1 80° 00' - 
: sin. GHI 40 00 - 
: : IH 28 


9.99335 

9.80807 

1.44716 


11.25523 


GI 


- log. 1.26188 


To find the double area of the triangle IAB. 

As rad. - 
: sin. AIB 13° 45' - 

: : IA X IF, | [g . 

t 

: 2.1 AB 248.2 - 


10.00000 

9.37600 

log. 1.46937 
— 1.54943 


2.39480 


To find the double area of the triangle 1BC. 


As rad. - 

: sin. B1C 9° 15' - 
: : IB XIC, ; 


10.00000 

9.20613 

- log. 1.54943 

- — 1.47463 


: 2.1 BC 169.9 


2.20319 























CHAP. III. 


CONTENT OF LAND. 


159 


To find the double area of the triangle ICD. 


As rad. 

: sin. CID 19° 30' 
:: 1C X ID, | 

: 2.ICD, 306.15 - 


10.00000 

9.52350 

- log. 1.47463 
- 1.48780 


2.48593 


To find the double area of the triangle IDE. 


As rad. 

: sin. DIE 26° 30' 
:: IDxIE, 

: 2.IDE 305.007 - 


10.00000 

9.64953 

- log. 1.48780 
- 1.34698 


2.48431 


To find the double area of the triangle IEF. 


As rad. 

: sin. EIF 24° 00' 
:: IE X IF, \ jp 


10.00000 

9.60931 

- log. 1.34698 
- 1.13542 


: 2.IEF 123.511 


2.09171 


To find the double area of the triangle IFG. 


As rad. 

: sin. FIG 13° 30' 
:: IFxIG, J 

: 2.1FG 58.274 


10.00000 
9.36818 

- log. 1.13542 

- — 1.26188 


1.76518 






160 


CONTENT OF LAND. 


CHAP. III. 




To find the double area of the triangle I AG. 


As rad. - 
: sin. AIG 31° 30' 

::IAxIG, Hq 
: 2.IAG 281.412 - 


10.00000 

9.71809 

- log. 1.46937 

- — 1.26188 


2.44934 


2.IAB 

2.IBC 

2.ICD 

2.IDE 

Ch. 

248.2 

169.9 

306.15 

305.007 

2.IEF 

2.IFG 

2.IAG 

Ch. 

123.511 

58.274 

281.412 

2.IAGFEI 

463.197 

2.IABCDEI 

2.IAGFEI 

1029.257 

463.197 

2.ABCDEFGA 

566.060 



ABCDEFGA 

283.03 Ch. 

=21 A. 1 R. 8 P. 


The bearings and distances of the sides, if required, 
might readily be obtained. For, having found the dis¬ 
tances IA, IB, we have in the triangle IAB, two sides, 
and an included angle; whence the angle IAB and 
side AB may be found. The angle IAB applied to the 
bearing of IA, will give the bearing of AB. In the 
same manner the bearings and distances of the other 
sides may be found. 

example 2. 

Being required to calculate the area ol a held, the 
owner of which refuses permission to go on it, I choose 
two stations, F andG, in the adjacent land, from whence 







CHAP. III. 


CONTENT OF LAND. 


161 


all the angles of the field arc visible. The bearing and 
distance of the stations, and the bearings of the angles, 
from each station, are as follow. What is the area of 
the field ? 

The station G bears from the station F, N. 43° W. 
20 ch. 




Bearing. 


Bearings. 

FA 

N. 

25i° 

E. 

GA 

s. 

66° 

E. 

FB 

N. 

19 

w. 

GB 

N. 

23 

E. 

FC 

N. 

5 

W. 

GC 

N. 

38i 

E. 

FD 

N. 

16 

E. 

GD 

N. 

60J 

E. 

FE 

N. 

60i 

E. 

GE 

S. 

84 

E. 


Ans. 33 A. 1 R. 7 P. 
PROBLEM XIV. 

To find the area of a survey by protracting it , and dividing 
the plot into triangles and trapeziums. 

The method of doing this will be easily understood 
from the following examples. 

EXAMPLE i. 

Given the bearings and distances of the sides of a 
tract of land as follow: 1st. N. 50° E. 9.60 ch.; 2nd. S. 
32° E. 16.38 ch.; 3rd. S. 41° W. 6.30 ch.; 4th. West, 
8.43 ch.; 5th. N. 79° W. 10.92 ch.; 6th. N. 5° E. 
11.25 ch.; 7th. S. 83° E. 6.48 ch.; to the place of be¬ 
ginning. Required the area. 

Fig. 75, is a plot of this survey; and by drawing the 

lines as in the plot, it is divided into two trapeziums 

AGFE, AEDF, and a triangle BDC. Measure the 
X 

























162 


CONTENT OF LAND. 


CHAP. Ilk 


several bases and perpendiculars, on the same scale that 
was used in the protraction, and find the double areas 
of the triangle and trapeziums by probs. 2 and 6; the 
sum of these will be the double area of the survey. 

Bases Perpens. 

EG 16.68x | j =203.6628=2 AGFE 

EB 19.17 x | i)d 8 10 \ = 267 - 4215 = 2 AEDB 
BD 19.23X Cc 5.16 = 99.2268=2 BDC 

2)570.3111 cli.=2 ABCDEFG 

285.15555ch.=28A. 2 R. 21\ 
= the area required. 

EXAMPLE 2. 

The following field-notes are given to protract the 
survey and find the area. 

Ch. 

1. N. 15° 00' E. 20 

2. N. 37° 30' E. 10 

3. East 7.50 

4. S. 11° 00' E. 12.50 

5. South 13.50 

6. West 10. 

7. S. 36° 30' W. 10. 

8. N. 38° 15' W. 8.50 

Jins. 46 A. 2 R. 0 P, 




V 


CHAPTER IV. 


* 



LAYING OUT AND DIVIDING LAND. 

* 

PROBLEM I. 

To lay out a given quantity of land in a square form. 

RULE. 

r> 

Reduce the given quantity to chains or perches, and 
extract the square root, which will be the length of a 
side, of the same denomination to which the given 
quantity is reduced. 


EXAMPLES. 

1. Required the side of a square that shall contain 
9 A. 3 R. 28 P. 

40)28 Per. 


4)3.7 R. 


9.925 A.=99.25 Ch. 


99.25(9.96 Ch. the length of a side. 

81 


189)1825 

1701 


1986)12400 

11916 


484 






/ 

* 







164 


LAYING OUT AND DIVIDING LAND. 


CHAP. IV. 


2. Required the side of a square tract of land that 
shall contain 325 acres. Ans. 57 chains. ^4 


PROBLEM II. 


To lay out a given quantity of land in a rectangular form , 

having one side given. 

' / ^ ) 

, •' * A 

RULE. 

iJ , ^ 

Divide the given content by the length of the given 
side, the quotient will be the length of the required side. 

- r " •/ - “’t 

A 

EXAMPLES. * 

1. It is required to lay out 120 acres in a rectangular 
form, the length of one side being given, equal 100 
perches. 


Acres. 

120 

4 


480 

40 




1,00)192,00 


192 perches, the length of the other side. 


2. The length of a rectangular piece of land is 8 
chains; what must be its breadth, that the content may 
be 5 acres? 


Am. 6.25 chains.^ 




CHAP. IV. LAYING OUT AND DIVIDING LAND. . 

\ " m 

PROBLEM III. 

To lay out a given quantity of land in a rectangular form , 
having the length to the breadth in a given ratio . 

% B'gHr 

RULE. 

/ 

As the less number of the given ratio, 

Is to the greater; 

So is the given area, 

% To a fourth term.* * 

• ' V * « .tr 'i s < ) 

The square root of this fourth term will be the length 
required. Having the length, the breadth may be found 
by the preceding problem. Or it may be found in the 
same manner as the length. Thus, 

As the greater number of the given ratio, 

Is to the less ; 

So is the given area, 

To a fourth term. 

The square root of this fourth term will be the breadth 
required. 

EXAMPLES. 

V 

1. It is required to lay out 864 acres in a rectangular 
form, having the length to the breadth in the ratio of 5 
to 3. 

9 f: ‘ ' 

: C~ 

* Demonstration. Let ABCD, Fig. 85, be a rectangle, and 
ABFE and AHGD be squares on the greater and less sides respec¬ 
tively : then (1.6) AD : AE (AB) : : the rectangle AC : square AF. 
Also AB : AH (AD) : : the rectangle AC : square AG. Hence the 
truth of the rule is evident. 



166 LAYING OUT AND DIVIDING LAND. CHAP. IV. 

> 

864 A. = 138240 P. 

Sq. P. Sq. P. 

As 3 : 5 :: 138240 : 230400 
\/230400=480 Perches, the length required. 

Sq. P. Sq. P. 

As 5 : 3 :: 138240 : 82944 ^ 

y/ 82944=288 Perches, the breadth required. 

2. It is required to lay out 27 A. 3 R. 20 P. in a rect¬ 
angular form, having the length to the breadth in the 
ratio of 9 to 7. Arts . Length 75.725 P. Breadth 

58.897 P. ^ 

'■ * 

PROBLEM IV. 

-ft 

To lay out a given quantity of land in a rectangular form , 
having the length to exceed the breadth by a given differ¬ 
ence. 

RULE. 

To the given area, add the square of half the given 
difference of the sides, and extract the square root of 
the sum; to this root add half the given difference for the 
greater side, and subtract it therefrom for the less.* 

* Demonstration. Let ABCD, Fig. 86, be a rectangle ; in DC 
let DE be taken equal DA or BC, and let EC be bisected in F ; then 
(6.2) DF 2 =DC x DE+FC 2 =DC X AD+FC 2 =the rectangle AC 
-l-the square of half the difference of the sides DC, DA ; also DF+ 
FC=DC, the greater side, and DF—FC=DE or DA, the less side. 

This problem may be neatly constructed thus : take EC equal the 
given difference of the sides and bisect it in F; make EG perpendicular 
to EC and equal to the square root of the given area, and with the 
centre F and radius FG describe the arc DG meeting CE produced 
in D : make DA perpendicular to DC and equal to DE, and complete 
the rectangle ABCD, which will be the one required. Since (47.1.) 
FG 2 =EG 2 +EF 2 =the given area+the square of half the given dif¬ 
ference of the sides, the truth of the construction is plain from the 
preceding demonstration. 


















w 
'i ■> 


CHAP. IV. LAYING OUT AND DIVIDING LAND. 


167 




EXAMPLES. 

4 * 

1. It is required to lay out 47 A. 2 R. 16 P. in a rect¬ 
angle, of which the length is to exceed the breadth by 
80 perches. 

2)80 P. 47 A. 2 R. 16 P.-7616 Per. 

— 1600 
40 - 

/ * 

40 

' _ \ 

1600 


v/9216=96 
half diff. add and subtract 40 


length 136 


breadth 56 

2. It is required to lay out 114 A. 2 R. 33.4 P. in a rec¬ 
tangular form, having the length to exceed the breadth 
by 15.10 chains. A ns. Length 42.25 ch. Breadth y* 

27.15 ch. / 

PROBLEM V. 

\' 4 

To lay out a given quantity of land in the form of a triangle 
or parallelogram , one side and an adjacent angle being 
given . 

RULE. 


For a triangle. 

O 

F 

As the rectangle of the given side and sine of the 
given angle, 

Is to twice the given area; 

So is radius, 

To the other side adjacent to the given angle. 

Then having two sides and the included angle given, 
the other angles and side, if required, may be found 
by trig, case 3. 





If * 


168 LAYING OUT AND DIVIDING LAND. CHAP. IV. 

For a parallelogram. 

As the rectangle of the given side and sine of the 
given angle, 

Is to the given area; * / ' || 

So is radius, 

To the other side adjacent to the given angle.* 


EXAMPLES. 

• ! ) •' 

1. Let AB, BC, Fig. 87, be two sides of a tract of 
land; the bearing of AB is S. 87W. dist. 16.25 ch. 
and the bearing of BC, N. 27 h° E.; it is required to lay 
off 10 acres by a straight line AD, running from the 
point A, to the side BC. 

Bearing of BA, N. 87T E. 

- . BC, N. 27i E. 


Angle B, 60° 

As ABy sin B $ 16.25 ch. 

As Atfxsm.45 ^ gin B 6QO 

: twice the given area 200 sq. ch. 
:: rad. - 


Ar. Co. 8.78915 

- 0.06247 

2.30103 

10.00000 


: BD 14.21 ch. 


1.15265 


* Demonstration. It is demonstrated, prob. 3. chap. 3, Measu¬ 
ring Land, that rad. : sin. 8 : : AB X BD : 2. ABD (see Fig. 87; ) 
therefore (1.6 cor.) rad. X AB : sin. B X AB : : AB x BD : 2. ABD, 
or (16.5) sin. B X AB : 2. ABD : : rad. X AB : AB X BD : : rad. : 
BD. Since ABDF is equal to 2. ABD, the truth of the rule for the 
parallelogram is evident. 

This problem may be constructed as follows ; take AB equal the 
given side and draw BC making the angle B equal to the given angle ; 
make BE perpendicular to AB and equal twice the given area of the 
triangle divided by the given side, or equal the given area of the par¬ 
allelogram divided by the given side ; and parallel to AB, draw EF 
cutting BC in D, join DA, then will ABD be the triangle required ; 
or complete the parallelogram ABDF, for the one required. The 
reason of the construction is plain. 









CHAP. IV. 


LAYING OUT AND DIVIDING LAND. 


169 


2. Given the side AB, Fig. 15, of a parallelogram, 
equal 20 ch. and the angle A 63° 30'; required the side 
AC, that the content may be 214 acres. 


» ip . • \ S AB 20 ch. 

AsABxsin-A j gin A6;jo 3(y 

: the given area 215 sq. ch. 

: : rad. - 


Ar. Co. 8.69897 

- 0.04821 

2.33244 

10.00000 


: AC 12.01 ch. 


1.07962 


3. Given one side of a triangle, equal 30 perches, an 
angle adjacent to this side 71° 15', and the area 2 acres; 

^required the other side adjacent to the given angle. 

Ans . 22.53 perches. 

4. Given one side of a parallelogram, equal to 32.26 

ch., an angle adjacent to this side 83° 30', and the area 
74 acres; required the other side adjacent to the given 
angle. Ans. 23.09 ch.'A 

PROBLEM VI. 

The area and base of a triangle being given , to cut of a 
given part of the area by a line running from the angle 
opposite the base. 

a 

RULE. 

* 

* 

As the given area of the triangle, 

Is to the area of the part to be cut off; 

So is the given base, 

To the base corresponding to that area.* 


* The truth of this rule is manifest from 1.6. 


Y 







I 


170 LAYING OUT AND DIVIDING LAND. CHAP. IV. 

EXAMPLES. 

1. Given the area of the triangle ABC, Fig. 88, equal 
650 square perches and the length of the base AB 40 
perches; it is required to cut oft 290 perches towards 
the angle A, by a line running from the angle C to the 
base. 

ABC. ADC. AB. AD. 

As 650 : 290 : : 40 : 17.85 per. 

2. In a triangle ABC, there are given the area 27 A. 

1 R. 16 P. and the base AB 35.20 ch., to cut off* 10 acres 
towards the angle B, by a line CD running from the 
angle C to the base: the part BD of the base is re¬ 
quired. Ans. 12.87 ch. ^ 

PROBLEM VII. 

The area and two sides of a triangle being given , to cat off 

a triangle containing a given area , by a line running from 

a given point in one of the given sides and falling on the 

other. 

\ 

RULE. 

As the given area of the triangle, 

Is to the area of the part to be cut off; 

So is the rectangle of the given sides, 

To a fourth term. 

Divide this fourth term by the distance of the given 
point from the angular point of the two given sides; the 
quotient will be thp distance of the required point from 
the same angle.* 

* Demonstration. From the demonstration to prob. 3, chap. 3, 
we have, Fig. 89. rad. : sin. A : : AB X AC : 2. ABC and rad. : 
sin. A : : AP X AG : 2.APG; therefore (11 &. 16.5) 2. ABC : 
2.APG : : ABxAC : APxAG, or (15.5), ABC : APG : : AB 
x AC : AP X AG ; hence the truth of the rule is manifest. 


> 



CHAP. IV. 


LAYING OUT AND DIVIDlNC LAND. 


171 


EXAMPLES. 


1. Given.the area of the triangle ABC, Fig . 89, 5 
acres, the side AB 50 perches, the side AC 40 perches, 
and the distance of a point F from the angle A, 36 
perches, it is required to find a point G to which, if a 
line be drawn from the point P, it shall cut off a triangle 
APG containing 3 A. 0 R. 20 P. 


As the triangle ABC 800 sq. 
: the triangle APG 500 


:: AB X AC, 

I 



50 - 
40 - 


P- 


: APxAG 

AP 36 


AG 34.72 per. 


Ar. Co. 7.09691 

2.69897 

1.69897 
1.60206 


3.09691 
log. 1.55630 


1.54061 


2. Given the area of a triangle ABC, 12 A. 1 R. 23 P. 
the side AB 20 ch., the side AC 16.25 ch., and the dis¬ 
tance of a point P in the side AB, from the angle A 8.50 
ch.; it is required to find the distance AG of a point G 
in the line AC, so that a line drawn from P to G may 
cut off a triangle APG containing 3 acres. Ans. 9.25 ch. 

PROBLEM VIII. 

The area and base of a triangle being given , to cut off a 
triangle containing a given area by a line running paral¬ 
lel to one of the sides. 

RULE. 

As the given area of the triangle, 

Is to the area of the triangle to be cut off; 

So is the square of the given base, 

To the square of the required base. 




172 


LAYING OUT AND DIVIDING LAND. 


CHAP. IV. 


The square root of which will be the base of the re¬ 
quired triangle.* 


EXAMPLES. 

% 

1. Given the area of the triangle ABC, Fig. 90, 500 
square perches, and the base AB 40 perches; it is re¬ 
quired to cut off 120 sq. per. towards the angle A, by a 
line DG running parallel to the side BC. 


As the triangle 
: the triangle 

: : AB 2 


ABC 500 
ADG 120 
SAB 40 
i AB 40 


Ar. Co. 7.30103 

- 2.07918 

- 1.60206 
- 1.60206 


: AD* 


- 2)2.58433 


AD 19.6 per. 


1.29216 


2. Given the area of a triangle ABC, 10 acres, and 
the base AB 25 ch., to find BD a part of the base, so 
that a line DG running from the point D, parallel to the 
side AC, may cut oft* a triangle BDG containing 4£ 
acres. A ns. BD—16. 77 ch/j^L * 


* The truth of this rule is manifest from 19.6. 

^ This problem may be neatly constructed as follows: Let ABC, 
Fig. 90, be the given triangle and AB the given base ; on AB de¬ 
scribe the semicircle AEB, and take AF to AB in the ratio of the 
part to be cut off, to the whole triangle ; draw FE perpendicular to 
AB, meeting the semicircle in E, join AE, and make AD equal to AE; 
from D draw DG parallel to BC and the thing is done. For, join EB 
and we have, by similar triangles, AB : AE : : AE : AF ; there¬ 
fore (20.6 cor. 2.) AB : AF : : AB 2 : AE 2 (AD 2 ) : : [19.6] 
ABC : ADG. . 

t If it be required to produce two sides of a given triangle so far 
that the triangle formed by these sides produced, and a line drawn be¬ 
tween them parallel to the third side, may contain a given area, it may 
be done by the above rule. Thus, Fig. 90, ADG : ABC : : AD 2 
; AB 2 . 





CHAP. IV. 


LAYING OUT AND DIVIDING LAND. 


173 


PROBLEM IX. 

The hearings of two adjacent sides , AD, AE, Fig. 91, 0 /a 
tract of land being given , to cut off a triangle ABC con¬ 
taining a given area by a line BC running a given course . 

RULE. 

From the given bearings of the lines, find the angles 
A, B, and C; then, 

As the rectangle of the sines of the angles A and B, 
Is to the rectangle of radius and sine of the angle C; 
So is twice the given area, 

To the square of the side AB. # 

In like manner the other sides may be found; or 
having found one side, the others may be found by trig, 
case 1. 

EXAMPLES. 

1. Let the bearing of AD, Fig. 91, be N. 87° 30' E. 
and of AE, N. 27° 30' E.; it is required to cut off 10 
acres by a line BC running N. 38° W. 


* The truth of this rule is evident from the demonstration to prob. 
4. chap. 3. 

Construction. Draw AD, AE, Fig. 92, according to the given 
bearings, and in AD take AF equal the square root of the given 
area, and on it describe the square AFGH ; make IE=AI, and draw 
ED of the same bearing as the division line BC, meeting AD in D ; 
on AD describe a semicircle, and produce GF to meet it in K, join 
AK and make AB equal to it; draw BC parallel to DE, and ABC 
will be the triangle required. For join IF, EF and KD, then (31.3, 
and cor. 8.6) AD : AK (AB) : : AK (AB) : AF; or (cor. 19.6.) 
AD : AF : : ADE : ABC, but (1.6) AD : AF : : ADE : AFE ; 
therefore (11.5.) ADE : ABC : : ADE : AFE, and consequently 
(9.5.) ABC=AFE; but because AI=IE, AFE=2.AFI=(41.1.) 
AFGH ; therefore ABC=AFGH=the givefl area of the triangle. 



174 


LAYING OUT AND DIVIDING LAND. 


CHAP. IV. 


AD, N. 87° 30' E. DA, S. 87° 30' W. EA, S. 27° 30' W. 

AE, N. 27 30 E. BC, N. 38 00 W. CB, S. 38 00 E. 

Angle A 60 00 125 30 Angle C 65 30 

180 00 


Angle B 54 30 

0.06247 
0.08931 
9.95902 
10.00000 
2.30103 


: AB S .2)2.41183 

AB 16.07 . 1.20591 


. . . t> S A 60° 00' Ar. Co. 

As sm. A. X sin. B, < g 00 _ 

, • ^ <C 65 30 •. - 

: rad. X sm. C, j rad . . . 

:: twice the given area, 200 sq. ch. 


2. Given the bearing of one side of a tract of land, 
S. 53° 15' E., and the bearing of an adjacent side taken 
at the same angle, N. 55° 00' E., to cut off 4 acres by a 
line running N. 4° 00' W.; required the distance on the 

“ 9,6 ch ^ 

PROBLEM X. 


/ 


The bearings of three adjacent sides , EA, AB, WT,fig. 93, 
or 94, of a tract of land, and the length of the middle side 
AB, being given, to cut off a trapezoid ABCD, contain¬ 
ing a given area, by a line DC , parallel to AB. 


RULE. 


From the given bearings find the angles A and B; 
add these together and take the difference between 
their sum and 180°, and call it P. Then, 


As the product of the sines of A and B, 

Is to the product of radius and sine of P; 









CHAP. IV. LAYING OUT AND DIVIDING LAND. 


175 


So is twice the area to be cut off’, 

To a fourth term. 

When the sum of the angles A and B is greater than 
180 ° add this fourth term to AB 2 ; but when the sum of 
these angles is less than 180 °, take the difference be¬ 
tween this fourth term and AB 2 . The square root of 
the result will be DC. Then, 

»„ ' /'i $[ B' .. 

As the sine of P, 

Is to the sine of B, 

So is the difference between DC and AB, 

To AD * 


* Demonstration. Produce EA and FB, Fig. 95, to me6t in P. 
Then (19.6) PDC : PAB :: CD 2 : AB 2 , or (17.5) ABCD : PAB 
:: CD 2 —AB 2 : AB 2 , or (A.5) PAB : ABCD :: AB 2 : CD 2 
—AB 2 ,or (15.16.5) 2.PAB : AB 2 :: 2.ABCD : CD 2 —AB 2 . But 
by the demonstration to prob. 4, chap. 3, 2.PAB : AB 2 : : sin. A. 
Xsin. B : rad. xsin. P. Consequently (11.5,) 

sin. Ax sin. B : rad. Xsin. P : : 2.ABCD : CD 2 —AB 2 . 

Now it is plain that AB 2 , added to this fourth term, gives CD 2 . 
A similar demonstration applies when the sum of the angles A and B 
is less than 180° as in Fig. 94. The latter part of the rule does not 
require demonstration. 

Construction. Draw AG, Fig. 93, perpendicular to AB, and 
make it equal to the quotient of twice the given area divided by AB. 
From I, draw IH parallel to AB, meeting EA and BF, in G and H, 
and on GH, describe the semicircle GMH. From A, draw AL 
parallel to BF ; and make LM perpendicular to GH. With the dis¬ 
tance HM and centre H, describe the arc MN ; and from N, draw 
ND parallel to AL. Lastly, draw DC parallel to AB, and it will be 
the division line required. For join BD, BG, and CG, Fig, 95. 
Then by similar triangles PG : PD : : GH : DC : : GH : HM : : 
HM : I1L : : DC : XB : : PC : PB. Hence (3.6) CG is paral¬ 
lel to BD ; and consequently tlie triangle BDC is equal to BGD. To 
each of these, add ABD. Then we have ABC=ABG. But it is 



176 


LAYING OUT AND DIVIDING LAND. 


CHAP. IV. 


EXAMPLES. 

1. Given the bearing of EA, Fig. 93, West, AB, N. 
10° E. dist. 15 ch.; and BF, N. 58° 30' E. to cut off 10 
acres by a line CD, running parallel to AB. Required 
the length of the division line and the distance AD. 

AE, N. 90° E. BF, N. 58° 30' E. A 80° 0' 


AB, N. 10 E. 

BA, S. 10 0 

W. B 131 30 

A = 80° 

48° 30 
180 0 

211 30 

180 0 


B=131 30 

P=31° 30' 

A • A , ■ n(A 80° 00' 

As sin. A.xsin. B < ^ 

d i . • |3 (Rad. - 

: Rad. X sin. r. j p 3Q 

:: twice the given area 200 sq. ch. 

Ar. Co. 0.00665 
0.12554 
- 10.00000 
9.71809 
2.30103 

: fourth term 

141.68 

2.15131 


AB 2 =:225. 


DC= \J 306.68=19.15 ch. 

As sin. P. 31° 30' - Ar, Co. 0.28191 

: sin. B. 131 30 - - 9.87446 

:: DC—AB 4.15 - - - 0.61805 

: AD 5.95 - - - 0.77442 


plain from the construction that ABG is equal to the given area. 
Hence ABCD is equal to the given area. 

When the sum of the angles A and B is less than 180°, as in 
Fig. 94, the semicircle must be described on AB ; the point L must 
be determined by drawing GL parallel to FB : and the arc MN must 
be described with the radius BM and centre B. The other parts of 
the construction are the same as before. 













CHAP. IV. LAYING OUT AND DIVIDING LAND. 177 

* V 

2. Given the bearings of three adjacent sides of a 
tract of land and the length of the middle one as follow; 
1st. N. 20° W.; 2nd. N. 60° 30' E. dist. 6 ch.; 3rd. S. 
61° 30' E.; to cut off a lot containing 2F acres, by a 
line parallel to the 2nd. side. Required the length of 
the division line and the distance on the 1st. side. 

A ns. Division line 8.70 ch.; distance on 1st. 

side 3.45 ch. 

3. Given as follow; . 1st. side N. 31° 15'W.; 2nd. 

N. 58° 45' E. dist. 13.50 ch.; 3rd. S. 14° 45' E.; to cut 
off 8 acres by a line parallel to the 2nd. side. The 
length of the division line and the distance on the 1st. 
side are required. Ans . Division line 11.61 ch.; dis¬ 

tance on the 1st. side 6.38 ch. 

« ’ . f t 

k / 

PROBLEM XL 

The hearings of three adjacent sides EA, AB, BF, Fig . 96, 
of a tract of land , and the length of the middle side AB 
being given , to cut off a trapezium ABCD containing 
a given area , by a line CD, running a given course. 

• 

PtULE. 

✓ j 

Draw AS parallel to BF, meeting CD or CD pro¬ 
duced, in S. From the given bearings, find the interior 
angles A, B, C, and D; add A and B together, and take 
the difference between their sum and 180°, and call it 
P. Then, 

*• • 

p , . 

As the product of the sines of C and D, 

Is to the product of radius and sine of P; 

So is twice the area to be cut off, 

To a fourth term. 

Z 


CHAP. IV. 


178 LAYING OUT AND DIVIDING LAND. 

Also, As the product of the sines of C and D, 

Is to the product of the sines of A and B; 

So is AB 2 , 

. . 

To a fourth term. 

When the sum of the angles A and B, is greater than 
180 °, add these two fourth terms together; but when 
the sum of these angles is less than 180 °, take the differ¬ 
ence of the fourth terms. The square root of the result 
will be CD. Then, 

As, sin. C : sin. B : : AB : CS. 

The difference between CD and CS, gives DS. Then, 
As, sin. P. : sin. C : r DS : AD. # 


* Demonstration. Produce EA and FB, Fig. 97, to meet in P ; 
draw AR and BU, each parallel to CD, and let VW, also parallel to 
CD, make the triangle PVW equal to PAB. Then (15.6) PA : PV 
: : PW : PB ; but (4.6) PA : PV : : AR : VW, and PW : PB 
: : VW : BU. Therefore (11.5) AR : VW : : VW : BU, and 
hence (17.6) ARxBU=VW 2 . But by trigonometry, 

As sin. ARB (sin. C) : sin. B : : AB : AR, 
sin. AUB (sin. D) : sin. A : : AB : BU. 

Hence (23.6.) As sin. C X sin. D : sin. A X sin. B : : AB 2 : AR X BU, 
Or, sin. CXsin. D : sin. AXsin. B : : AB 2 : VW 2 . 

And by the demonstration to the rule in the last problem, we have 
sin. CXsin D : rad. Xsin. P : : 2.ABCD : CD 2 —VW 2 . 

The sum of these fourth terms gives CD 2 . The demonstration is 
similar, when the sum of the angles A and B is less than 180°. 

Construction. From B, Fig. 96, draw BU according to the re¬ 
verse bearing of the division line DC, meeting EA or EA produced in 
U. Make AI perpendicular to AB, and equal to the quotient of twice 
the given area, divided by AB. Draw IG parallel to AB ; GH 
parallel to BU ; and UL parallel to BF. On GH, describe the 
semicircle GMII and make LM perpendicular to GH ; with the ra¬ 
dius HM and centre H, describe the arc MN; and from N, draw 


« 




CHAP. IV. 


LAYING OUT AND DIVIDING LAND. 


179 


EXAMPLES. 

# • % 

> f 

1. Let the bearings of EA, Fig. 96, be N. 80° 30' 
W.; AB, North, dist. 12 ch.: and BF, N. 58° E.; it is 
required to cut off 10 acres by a line DC, running N. 

CB, S. 58° 00' W. 

CD, S. 14 30 E. 

• _ 

C=72° 30' 


A = 99° 30' 
B=122 00 


221 30' 

180 00 

P— 41 30 

Ar. Co. 0.02058 

- 0.03927 

- 10.00000 

- 9.82126 

- 2.30103 


2.18214 


ND parallel to UL. From D, draw the division line DC parallel 
to BU. 

When the sum of the angles A and B is less than 180 °, the semi- 
circle must be described on BU ; the point L must be determined by 
drawing GL parallel to BF, and the arc MN must be described with 
the radius BM and centre B. 

The demonstration is exactly the same as that for the construction 
of the last problem. 


14° 30' W. 

AE, S. 80° 30' E. BF, N. 58° E. 
AB, N. 0 00 E. BA, S. 0 E. 


80 30 
180 0 


58 

180 


A= 99° 30' 


B=122 


DA, N. 80° 30' W. 
DC, N. 14 30 W. 


D=66° 00' 


a ■ n • r> S C 72 ° 30' - 

As sin. C X sin. D < ^ gg 00 

: rad. x sin. P. j g 0 ’ 

:: twice the given area 200 sq. ch. 

: fourth term 152.1 















180 


LAYING OUT AND DIVIDING LAND. 


CHAP. IV- 


C 72° 30' 
D 66 00 
A 99 30 
B122 00 
AB12 - 
AB 12 - 

: fourth term 138.24 
fourth term 152.10 

DC=. sj 290.34=17.04 


As sin. Cx sin. D 

l 

: sin. Ax sin. B. 

:: AB S 


Ar. Co. 0.02058 
- 0.03927 

- 9.99400 

- 9.92842 

- 1.07918 

- 1.07918 


- .2.14063 


As sin. C 72° 30' 
: sin. B 122 00 
:: AB 12 

: CS 10.67 - 
DC 17.04 

DS 6.37 


Ar. Co. 0.02058 
9.92842 
1.07298 q 

1.02818 


As sin. P 41° 30' 


Ar. Co. 0.17874 


: sin,C 72 30 . 9.97942 

:: DS 6.37 - - - ' - - - 0.80414 


: AD 9.17 . 0.96230 

I 

2. Given the bearings of three adjacent sides of a 
tract of land and the length of the middle one as follow: 
1st. N. 31° 15' W.; 2nd. N. 58° 45' E. dist. 13.50 ch.; 
3rd. S. 14° 45' E.; to cut off 8 acres by a line from the 
1st. side to the 3rd. running S. 87° 30' E.: required the 
length of the division line and the distance on the 1st. 
side. Ans. Division line 12.75 ch.; distance 1st. 

side 2.69 ch. 


3. Given as follow; 1st. side, N. 74° 45'W.; 2nd. 
N. 37° E. dist. 17.24 ch.; 3rd. N. 84° E.; to cut off a 
field containing 20 acres, by a line from the 1st. side to 








CHAP. IV. 


LAYING OUT AND DIVIDING LAND. 


181 


the 3rd. running N.*20° E. The length of the division 
line and the distance on the 1st. side are required. 

Ans. Division line 19.68 ch.; 
distance on 1st. side 14.01 ch. 

• « 



PROBLEM XII. 


The bearings of several adjacent sides , EA, AV, VW, WX, 
XB, BF, Fig. 98, of a tract of land , and the distance of 
each , except the first and last , being given , to cut of a 
given area , by a line DC, running a given course. 

j . RULE. 

V 

-♦ t • V • . , • 

Join AB and calculate the area of AVWXBA, and 
the bearing and distance of AB. Subtract the area of 
AVWXBA from the area to be cut off, the remainder 
will be the area of ABCD. Then with the bearings of 
EA, AB, BF, DC, the distance AB, and the area of 
ABCD, proceed as in the last problem. 

EXAMPLES. 

1. Let the bearing of EA, Fig. 98, be N. 48° 30' W. 
AV, S. 78° W. dist. 8 ch.; VW, N. 26° 30' W. disk 
11.08 ch.; WX, N. 38° 30' E. dist. 12.82 ch.; XB, S. 
64° E. dist. 10.86 ch.; and BF, S. 86° E. It is required 
to cut off 30 acres by a line DC, running N. 32° 15' E. 


Stat. 

Bearing. 

Dist. 

N. 

S. 

E. 

W, 

EDD 

W. 

D.D. 

Multi¬ 

pliers. 

N. 

Ar. 

S. Areas. 

AV 

S. 78°W. 

8.00 


1.66 


7.83 


12.79 

0.00E 



VW 

N.26£W. 

11.08 

9.91 



4.95 


12.78 

12.78W 


126.6498 

WX 

N.38£ E. 

12.82 

10.03 


7.98 


3.03 


9.75W 


97.7925 

XB 

S. 64 E. 

10.86 


4.76 

9.76 


17.74 


7.99E 


38.0324 

BA 




(13.52) 


(4.96) 

4.80 


12.79E 


172.9208 

• 



19.94 

19.94 

17.74 

17.74 

25.57 

25.57 



435.3955 

Sq. cl). 217.69775 








































































182 


LAYING OUT AND DIVIDING LAND. CHAP. IV, 


Area to be cut off 300 
Area of AVWXBA 217.69775 


Area of ABCD 82.30225 


diff. of lat. of BA, 13.52 S. 

: dep. do. - 4.96 W. 

:: rad.. 

: tang, of bearing of BA, S. 20 9' W. 


Ar. Co. 8.86902 
0.69548 
10.00000 

9.56450 


As rad. 

: sec. of bearing 
:: diff. of lat. 

: BA 14,40 


Ar. Co. 0.00000 
20° 9' - 10.00743 

13.52 - - - >' 1.13098 

- . - - 1.13841 


The angles, found from the bearings, are A= 111 0 2T, 
B=106° 9', C=61° 45', D=80° 45' and P=37° 30'. 


As sin. C x sin. 


n < C 61° 45' 
l '' ’ l D 80 45 - 

: rad. x sin. P. $ p l< ' j _ " 0 " 

:: twice the area ABCD. 164.6 sq. ch. - 


Ar. Co. 


0.05508 

0.00568 

10.00000 

9.78445 

2.21643 


: fourth term 115.25 


2.06164 


As sin. C.xsin. D, 
: sin. Ax sin. B, 
:: AB S 


< C 61° 45' 
(D 80 45 
s A 111 21 
(B 106 9 
^ AB 14.40 
(AB 14.40 


Ar. Co. 0.05508 

- 0.00568 

9.96912 
9.98215 
- i 1.15836 
1.15836 


: fourth term 213.36 
do. 165.25 


2.32911 


DC= y/ 328.61 =18.13 










CHAP. IV. 


LAYING OUT AND DIVIDING LAND. 


3 83 


As sin. C 61° 45' At. Co. 0.05508 
: sin. B 106 9 9.98251 

:: AB 14.40 - - - 1.15836 

# i ! 

: CS 15.70 - - 1.19595 

t * 

* • 

As sin. P 37° 30' Ar. Co. 0.21555 

: sin. C 61 45 - - - 9.94492 

:: DS 2.43 - - - 0.38561 

: AD 3.52 .... 0.54608 

2. Given as follow; 1st. side, N. 62° 15' W.; 2nd. N. 
19° E. dist. 18 ch. ; 3rd. S. 77° E. dist. 15.25 ch. ; 4th. 
S. 27° E*. ; to cut of 35 acres by a line, from the first 
side to the last, running N. 82° 30' E. Required the 
length of the division line, and the distance on the first 
side. Ans. Division line 22.99 ch.; distance on 1st. 

side 5.14 ch. 

PROBLEM XIII, 

The hearings of several adjacent sides , AB, BC, CD, DE, 
Fig 99, of a tract of land , and the distance of each , ex¬ 
cept the last , being given , to cut off a ^ven area hy a line 
AH running from the angle A and falling on the side DE. 

RULE. 

By Prob. 9. Chap. I, change the bearings of all the 
given sides, so as to make the side, on which the divi¬ 
sion line is to fall, a meridian. 

With the given distances and changed bearings, find 
the corresponding differences oflatitude and departures; 
add together the numbers in each departure column, 
and take the difference of their sums, which will be the 




184 LAYING OUT AND DIVIDING LAND. CHAP. IV. 

departure of the division line, and must be placed in the 
proper column, opposite said line. Then having all the 

departures, find the double departures, as in Prob. 11. of 

. _ • 

the last chapter. Find also the multipliers, beginning 
with the one to correspond \Vith th« division line, and as¬ 
suming it 0; multiply the known differences of latitude 
by their corresponding multipliers and place the pro¬ 
ducts in the proper columns of north and south areas. 

Add together the products in each of the columns of 
areas, and subtract the less sum from the greater; take 
the difference between the remainder and double the 
area to be cut off, and divide it by the multiplier cor¬ 
responding to the side on which the division line is to 
fall; the quotient will be the difference of latitude of 
this side, which place against it, in the column of north 
or south latitude, according as its changed bearing is 
north or south. Then add together the numbers in 
each latitude column and take the difference of their 
sums, which will be the difference of latitude of the 
division line, of the same name with the less sum. 

With the difference of latitude and the departure of 

the division line, find by Prob. 10. Chap. 1, its changed 

bearing and its distance. Then find the true bearing 

by note to the rule in Prob. 9, Chap. 1.* 

0 

EXAMPLES. 

1. Let the bearing of AB be N. 62T W. 14.75 ch.; 
BC, N. 19° E. 27 ch.; CD, S. 77° E. 22.75 ch.; and 
DE, S. 27° E.; it is required to cut off 70 acres by a line 
AH, running from the angle A and falling on the side 
DE. 


* The reason of this rule is sufficiently obvious without a demon¬ 
stration. 





CHAP. IV. LAVING OUT AND DIVIDING LAND. 


185 


05 05 
CO CO I 
CO CO | 
CO £>. 


tO tO 
Cn <1 
>£>. • 
CO CO I 
-J cn 


to 

CO 

Jo 

CO 

£3'co 

CO 

CO o 
CO v 

CO 

cn 


So? 

CO rf 
05 ^ * 

O 



HA 

DH 

CD 

BC 

> 

to 

Sta. 

1 


U2 

to 

H 

S 77 E 

N 19 E 

3 

05 

to 

4 ->- 

o 

3 

Bearing's. 



South 

S 50 E 

N 46 E 

52! 

CO 

cn 

o 

3 

Changed 

Bearings. 




to 

to 

Cn 

to 

-V 

o 

o 

i—* 

Cn 

Dist. 

30.80! 




12.04 

18.76 

N. 

CO 

o 

CO 

o 

k) 

(10.96) 

14.62 



m 

• 

08 

05 

CO 



17.42 

19.42 


E. 

36.84 

(28.33) 




• 8.51 

W. 

65.17 


17.42 

CO 

X* 

o 


EDD 

05 

Cn 

• 

-1 

. w 
•w 




CO 

F> 

CO 

45. 

• ^ 

O- 

• 


’ o 

b 

o 

W 

i 

to 

CO 

If 

CO 

M 

10.91E 

to 

cn 

‘49 

CO 

3 

36.84W 

Multi¬ 

pliers. 







N. Ar. 

1089.5046 

1 

1 

159.5042 . 

486.4468 

443.5536 

S. Areas. 


As diff. lat. of HA, 5.22 S. - Ar. Co. 9.28233 
dep. do. 28.33 W. - 1.45225 

: rad. - - *. 10.00000 


tang, changed bear, of HA, S. 79° 34' W. 10.73458 

Subtract 27 00 


True bearing of HA, S. 52 34 W. 

A a 

























































































186 LAYING OUT AND DIVIDING LAND. CHAP. IV. 

f 

As rad. ----- Ar. Co. 0.00000 
: sec. changed bearing of HA, 79° 34' - 10.74210 

:: diff. lat. 5.22 - - - - 0.71767 


: dist. AH 28.83 - 1.45977 

Hence AH bears N. 52° 34' E. dist. 28.83 ch. 

i 

2. Given as follow: 1st. side S. 78° W. 8 ch.; 2nd. 
N. 26i° W. 11.08 ch.; 3rd. N. 38£° E. 12.82 ch.; 
4th. S. 64° E. 10.86 ch.; 5th. S, 234° E.; to out off 25 
acres by a line running from the place of beginning and 
falling on the 5th side; required its bearing and dis¬ 
tance. Jins . N. 45° I' E. dist. 10.67 ch. 

PROBLEM XIV. 

* 

The sides AB, BC, CA, Fig. 100, of a triangular piece of 
ground being given , to divide it into two parts having a 
given ratio , by a line F E, running parallel to one of the 
sides as BC*. 


RULE. 

As the sum of the numbers expressing the ratio of 
the parts, 

Is to that number of the ratio which corresponds to 
the part to be adjacent to A; 

So is the square BC, 

To the square of FE. 

Then, As BC : AB :: FE : AF.* 


* Demonstration. Let m to n be the ratio of the part AFE to 
the part FECB ; then ( 18 . 5 ) m-\-n : m : : ABC : ADE : : ( 19 . 6 ) 
BC 2 : FE 2 . 

Construction. On AB describe the semicircle AMB, and by 
Prob. 17, Page 34, divide AB in K, so that AK may be to KB in the 
given ratio of the part AFE to the part FECB ; draw KM perpen- 





CHAP. IV. 


LAYING OUT AND DIVIDING LAND. 


187 


EXAMPLES. 

1. Let AB be 21.26 ch.; BC, 12.76 ch. ; and AC, 
19.30 ch.; it is required to divide the triangle by the 
line FE, parallel to BC, so that the part AFE may be 
to the part FECB as 2 to 3. 

As 5 : 2 : : 12.76 3 : FE 2 =65.12704. 

FE=z v 7 65.127048.07 
As 12.76 : 21.26 : : 8.07 : AF= 13.45 

2. The three sides of a triangular piece of land, ta¬ 
ken in order, measure 15,10, and 13 chains respective¬ 
ly ; it is required to divide it into two equal parts by a 
line parallel to the second side. What will be the 
length of the division line and its distance from the 
pl&ce of beginning, measured on the first side ? 

Ans. Division line 7.07 ch.; distance on 1st side 10.60 ch. 

PROBLEM XV. 

V 

The bearings and distances of the sides AB, BC, CA, Fig. 
101, of a triangular piece of ground being given, to di¬ 
vide it into two parts having a given ratio , by a line FE, 

running a given course. 

* « 

RULE. 

As the product of the sines of F and E, 

Is to the product of the sines of B and C; 


dicular to AB, meeting the semicircle in M, and with the radius AM 
and centre A, describe the q,rc MF. From F, draw the division line 
FE parallel to BC. Since, (35.3, and cor. 8.6) AB : AM (AF) : : 
AM (AF) : AK, we have (20.6 cor. 2.) AB : AK : : AB 2 : AF 2 :: 
ABC : AFE. Hence the truth of the construction is evident. 




V 


188 LAYING OUT AND DIVIDING LAND. CHAP. IV 

✓ 

So is the square of BC, 

To a fourth term. 

Multiply this fourth term by that number of the ratio 
which corresponds to the part to be adjacent to the 
angle A, and divide the product by the sum of the num¬ 
bers expressing the ratio. The square root of the 
result will be FE. Then, 

As sin. A: sin. E : : FE : AF. # 

r 

EXAMPLES. 

V 

1. Let the bearing of AB, be S. 82T E. dist. 14.17 
ch.; BC, N. 18f° W. 8.51 ch.; and CA, S. 61T W. dist. 
12.87 ch.; it is required to divide the triangle by the 
line FE, running N. 141° E. so that the part AFE may 
be to the part FECB in the ratio of 2 : 3. 

* Demonstration. Draw CG and BR, Fig. 102, each parallel 
to EF ; and let VW, also parallel to EF, make the triangle AVW 
equal to ABC. Then (15.6) AB : AV : : AW : AC ; but (4.6) 
AB : AV : : BR : VW, and AW : AC : : VW : GC. Therefore 
BR : VW : : VW : GC ; and hence (17.6) BRxGC=VW 2 . But 
by trigonometry, 

As sin. R. (sin. E) : sin. C : : BC : BR, 

sin. G. (sin. F) : sin. B : : BC : GC. 

Hence (23.6) sin. E X sin. F : sin. B X sin. C : : BC 2 : BR X GC 
: : BC 2 : VW 3 . 

Alsowi-f-n : m : : ABC : AFE : : AVW : AFE : : (19.6) VW 3 : 
FE 2 . 

Construction. From C, Fig. 101, draw CG according to the re¬ 
verse bearing of FE, and on AG describe the semicircle AMG. By 
prob. 17, page 34, divide AB in K, so that AK may be to KB in the 
given ratio of the part AFE to the part FECB. Draw KM perpen¬ 
dicular to AB, and with the radius AM and centre A, describe the 

arc MF. From F, and parallel to GC, draw FE the required division 
line. For join KC, Fig. 102 ; then (1.6) KC divides the triangle 
in the given ratio. Now AC : AE : : AG : AF (AM) : : (cor. 8.6) 
AM (AF) : AK ; therefore (1 1 . 5 ) A C : AE : : AF : AK, and hence 
(15.6) the triangle AFE is equal to AKC. Consequently FE di¬ 
vides the triangle in the given ratio. 

t 









( 


CHAP. IV. LAYING OUT AND DIVIDING LAND. 189^ 


Angle A—36£°, B=63}, C = 80i°, E=46*° and F=83°. 


As sin. E x sin. F, 

: sin. B x sin. C, 

: : BC 2 

( E 46° 45' 

(F 83 00 

3 B 63 30 - 

} C 80 15 - 

] BC 8.51 - 

( BC 8.51 - 

Ar. Co. 0.13765 

- 0.00325 

9.95179 

9.99368 

0.92993 

0.92993 

: fourth term 

88.35 

2 

1.94623 


5)176.70 


FE= 

: v/35.34=5.95 



As sin. A, 36° 15' 

- 

as 

- 

Ar. Co. 0.22819 

: sin. E. 

46 45 

- 

- 

- 

- 

9.86235 

: : FE 

5.95 - 

i' 

- 

mm 

- 

C^pp9 

: AF 

7.32 - 


. 

. 

mm 

0.86433 


2. The bearings and distances of a triangular piece 
of land ABC are, AB, S. 69° E. 21.40 ch.; BC, N. 31* 
E. 18.66 ch.; and CA, S. 74} W. 30.85 ch.; and it is 
required to divide it by a line FE, running due north, 
so that the part AEF, may be to the part FECB, as 4 
to 5. What will be the length of the division line FE, 
and the distance AF ? Ans, FE 10.74 and AF 17.40. 

PROBLEM XVL 

The hearings and distances of the sides AB, BC, CD, DA, 
fig . 103, of a trapezoidal tract of land being given , to 
divide it into two parts having a given ratio , by a line FE, 
running parallel to the parallel sides AB, CD. 

RULE. 

I 

Multiply the square of AB, by that number of the ra- 


i 







I 


< 


V 


190 LAYING OUT AND DIVIDING LAND. CHAP. IV. 

tio which corresponds to the part, to be adjacent to 
CD, and the square of CD, by the other number of the 
ratio. Add the two products together, and divide the 
sum by the sum of the numbers expressing the ratio. 
The square root of the quotient will give FE. Then, 
As DC—AB : FE—AB :: AD : AF* 

/ 

EXAMPLES. 

]. Let the bearing of AB be N 14° E. dist. 10 ch. BC, 
N. 55i° E. dist. 18.67 ch.; CD, S. 14° W. dist. 


* Demonstration. Produce DA and CB, Fig. 104, to meet in P. 
Then (19.6) PDC : PAB : : CD 2 : AB 2 , or (17.6) ABCD : : PAB 
:: CD 2 —AB 2 : AB 2 , or, (16.5) ABCD : CD 2 —AB 2 : : PAB : 
AB 2 ^In like manner ABEF : FE 2 —AB 2 : : PAB : AB 2 . Hence 
(11.5) )YBCD : CD 2 — AB 2 : : ABEF : FE 2 —AB a, or (16.5) 
ABIE ABEF : : CD"—AB 2 : FE 2 —AB 2 . Therefore m-\-n : 
m : : CD 2 —AB 2 : FE 2 —AB 2 , or multiplying extremes and means, 
m-\-n. FE 2 —m-fn. AB 2 =m. CD 2 -— m. AB 2 . But (m+n.) AB a 
=m. AB 2 +n. AB 2 . Therefore, adding equals to equals, we have 

m-\-n. FE 2 =wi. CD 2 -f-n. AB 2 . Hence the truth of the rule is 
evident. 

Construction. Join CA, Fig. 103, and parallel to it, draw BH, 
meeting DA produced, in H. Divide (prob. 17, page 34) HD in K, 
so that IIK may be to KD in the given ratio of ABEF to FECD, and 
draw KL parallel to BC. On CD, describe the semicircle CMD, 
and draw LM perpendicular to CD. With the radius CM and cen¬ 
tre C, describe the arc MN, and from N draw NF parallel to KL. 
From F, draw the division line FE parallel to AB or CD. For join 
KC, Fig. 104, and draw KU parallel to AB. Then since BH is par¬ 
allel to AC, the triangle AHC is equal to ABC ; and adding AHC to 
each, we have CHD=ABCD. Now (4.6) PC : PE : : CD : FE 
(CM) : : (cor. 8.6) CM (EF) : CL (UK) : : PF : PK. Therefore 
(11.5) PC : PE : : PF : PK ; and hence (15.6) the triangle PEF is 
equal to PCK. Consequently CKD=FECD. But it has been pro¬ 
ved that CHD ABCD ; hence taking equals from equals we have 
HCK=ABEF. But (1.6) HCK : CKD : : HK : KD : : m : n. 
Therefore ABEF : FECD : : m : n. 


t 








CHAP. IV. 


LAYING OUT AND DIVIDING LAND. 


191 


20.98 ch. and DA, W. 12.70 ch.; it is required to di¬ 
vide the trapezoid into two parts by a line FE, parallel 
to AB or DC, so that the part ABEF may be to the 
part FECD as 3 to 2. 

2. AB 2 -200. 

3. CD 2 —1320.4812 

5)1520.4812 

\ 

FE= y/ 304.0962=17.44 
As 10.98 : 7.44 : : 12.70 : AF=8.Gl 

2. The boundaries of a trapezoidal field ABCD are 
given as follow ; viz. AB, N. 80° W. 60 per.; BC, N. 
39s° W. 45.5 per.; CD, S. 80° E. 89.4 per.; and DA, 
S. 30 per.; and it is required to divide it into two equal 
parts by a line FE parallel to AB or CD. What will 
be the length of the division line FE, and the distance 
AF ? * fins. FE 76.13 per. and AF 16.46 per. 


PROBLEM XVII. 

> ' 

The bearings and distances of the sides AB, BC, CD, DA, 
Fig . 105, of any quadrilateral tract of la?id being given , to 
divide it into two parts having a given ratio , by a line 
FE, running parallel to one of the sides as AB or CD. 


RULE. 

Call the side to which the division line is to be par¬ 
allel, the parallel side; and the one opposite to this, the 
opposite side. From the bearings, find the angles. 
Take the difference between the sum of th<? angles ad¬ 
jacent to the parallel side and 180°, and call it P. Then, 




192 


LAYING OUT AND DIVIDING LAND. 


CHAP. IV. 


As the product of the sines of the angles adjacent to 
the parallel side, 

Is to the product of the sines of the angles adjacent 
to the opposite side ; 

So is the square of the opposite side, 

To a fourth term. / 

Multiply this fourth term by that number of the ratio 
which corresponds to the part to be adjacent to the 
parallel side, and to the product add the product of 
the square of the parallel side by the other number of 
the ratio; and divide the sum by the sum of the num¬ 
bers expressing the ratio. The square root of the 
quotient will be the length of the division line FE. 
Then, 

As the sine of P, 

Is to the sine of E ; 

So is the difference between FE and the parallel side, 
To the distance of F from the adjacent end of the 
parallel side.* 


* Demonstration. Produce DA and CB, Fig. 106 , to meet in P. 
Draw DR and CG each parallel to AB ; and let VW, also parallel to 
AB, make the triangle PVW equal to PCD. Then (15.6) PD : PV 
:: P W : PC. But ( 4 . 6 ) PD : PV :: DR : VW,andPW : PC :: VW 
: CG. Therefore (11.5) DR : VW : : VW : CG ; and hence (17.6) 
DR X CG=VW 2 . But by trigonometry, 

As sin. CRD (sin B) : sin. C : : CD : DR. 

sin. CGD (sin. A) : sin. D : : CD : CG. , ^ 

Hence (2.36) sin. A X sin. B : sin. C X sin. D : : CD 2 : DR X CG. 

Or sin. AXsin. B : sin. CXsim D : : DC 2 : VW a . 

But by the demonstration to the rule in the last problem, we have 
^N7FE 2 =m. VW 2 -H. AB 2 . 

Hence the truth of the rule is evident. 

Construction. From C, Fig. 105, draw CG parallel to AB, and 
on it describe the semicircle CMG. 




GHAP. IV. 


LAYING OUT AND DIVIDING LAND. 


193 


EXAMPLES. 

\ i 


1. Let the bearings of AB be North, 12 cli; BC, N. 
56|° E. 20.78 ch.; CD, S. 33>° E. 22.21 ch.: and DA, 
S. 804° W. 30 ch.; it is required to divide the tract 
into two parts by a line FE, parallel to AB, so that 
the part ABEF may be to the part FECD as 3 to 5. 
Angle A=804, B=1234°, C=90°, D=66°, and P= 


24°. 


As sin. A x sin. B, j g 
: sin. C x sin. D, 

: : CDs 


A 80° 30' 
123 30 
C 90 00 
D 66 00 
< CD 22.21 
$ CD 22.21 


fourth term 


547.92 

% 

3 


A 


Ar. Co. 0.00600 

- 0.07889 

10.00000 

9.96073 

1.34655 

1.34655 


2.73872 


1643.76 
5. AB”=720.00 


8)2363.76 


FE= y/ 295.47 
As sin. P 24° 00' 

: sin. E 123 30 
: : FE—AB, 5.19 

: AF 10.64 


17.19 

Ar. Co. 0.39069 
9.92111 

0.71517 

# : • - 

- *• 1.02697 


Join CA, and draw BH parallel to it meeting DA produced in H. 
Divide HD in K, so that HK may be to KD in the given ratio of the 
part ABEF to FECD. Draw Kl^parallel to BC and LM perpen¬ 
dicular to CG. With the radius CM and centre C, describe the arc 
MN. Draw NF parallel to KL and FE parallel to AB. Then will 
FE be the division lino. When the division line is to be parallel to 
CD, the semicircle must be described on CD ; and the line CG need 
not be drawn. The demonstration of the construction is the same as 

for the last problem. 

Bb 









194 


LAYING OUT AND DIVIDING LAND. 


CHAP. IV. 


2. The boundaries of a field ABCD are given as fol¬ 
low ; viz. AB, S. 10i° W. 7.20 ch. ; BC, S. 67° W. 12.47 
ch.; CD, N. 23° W. 13.33 ch.; and DA, S. 89° E. 18 
ch.; and it is to be divided into two parts by a line FE, 
parallel to the side AB, so that the part ABEF may be 
to the part FECD, as 3 to 4. Required the length of 
the division line FE, and the distance AF. 

Ans. FE 10.69 ch.; and AF 7.15 ch. 

3. Given the boundaries of a field the same as in th 

preceding example, to divide it into two parts by a 
line FE, parallel to the side CD, so that the part ABEF 
may be to the part FECD, as 3 to 4. Require FE 
and AF. Ans. FE 10.14, and AF 10.16. 

PROBLEM XVIII. 

The bearings and distances of the sides AB, BC, CD, DA, 
F«g. 107, of any quadrilateral tract of land being given , 
to divide it into two parts having a given ratio , by a line 
FE, running a given course from some point in AD to an¬ 
other in BC. 

RULE. 

From A, draw AS parallel to BC, meeting FE in S. 
From the bearings find the angles A, B, C, D, E, and 
F.* Take the difference between the sum of the an¬ 
gles A and B, and 180°, and call it P. Then, 

As the product of the sines of the angles E and F, 
: the product of the sines of the angles A and B, 
:: the square of AB, 

: a fourth term. 

Also, As the product of the sines of the angles E and F, 
: the product of the sines of the angles C and D; 

* It is immaterial whether it is the angle BEF or CEF, that is 
found, also whether, AFE or DFE. 







CHAP. IV. 


LAYING OUT AND DIVIDING LAND. 


195 


: : the square of CD, 

: to a fourth term. 

Multiply this latter fourth term by that number of the 
ratio which corresponds to the part to be adjacent to 
AB, and the other fourth term by the other number of the 
ratio; add the two products together, and divide the 
sum by the sum of the numbers expressing the ratio. 
The square root of the quotient will give the length of 
the division line FE. Now, 

As sin. E : sin. B :: AB : ES. 

The difference between FE and ES, gives FS. Then, 
As sin. P : sin. E : : FS : AF.* 


EXAMPLES. 


1. Let the bearing of AB, be north, dist. 12 ch ; BC, 
N. 56i°E. 20.78 ch.; CD, S. 33^° E. 22.21 ch.; and 
DA, S. 80£° W. 30 ch.; it is required to divide the 
tract into two parts by a line FE, running N. 20 ° W. so 


that the part ABEF may be to the part FECD as 3 to 5. 
Angle A—80±°, B=123^, C=90°, Dr=66°, E=76p>, 


F=69£° and P=r24°. 

A • v,, • J?S E 76° 30' 

As sin. E x sin. t < p 79 30 

A 80 30 
B 123 30 
AB 12 
AB 12 


: sin. A x sin. B, 
: : AB* 


Ar. Co. 0.01217 

- 0.00733 

9.99400 

9.92111 

1.07918 

1.07918 


: fourth term 123.87 

5 


2.09297 


619.35 


* The truth of this rule is evident from the demonstration to the 
rule in the last problem. 

Construction. Draw CG according to the reverse bearing of FE, 
and then proceed with the construction exactly as in the last problem. 








196 


LAYING OUT AND DIVIDING LAND. 


CHAP. IV. 


As sin.'E. x sin. F, 
: sin. C x sin. D, 

:: CD% 


I E 76° 30' 
F 79 30 
C 90 00 
D 66 00 
CD 22.21 
CD 22.21 


: fourth term 471.33 

3 


1413.99 

619.35 


8)2033.34 

FE= y/254.17= 15.94 
As sin. E, 76° 30' - 
:sin.B, 123 30 - 

:: AB 12 


Ar. Co. 0.01217 

- 0.00733 

10.00000 

9.96073 

1.34655 

1.34655 


2.67333 


Ar. Co. 0.01217 
9.92111 
1.07918 


♦ 

: ES 10.29 


1.01246 


As sin. P, 24° 00' 

: sin. E, 76 30 - 
: : FS 5.65 


Ar. Co. 0.39069 

- 9.98783 

- 0.75205 


: AF 13.51 . 1.13057 


2. The boundaries of a field ABCD arc given as fol¬ 
low; viz. AB, S. 10i° W. 7.20 ch.; BC, S. 67° W. 12.47 
ch.; CD, N. 23° W. 13.33 ch.; and DA, S. 89° E. 18 ch; 
and it is to be divided into parts ABEF and FECD, in 
the ratio of 3 to 4, by a line FE, running due South. 
Required the length of the division line FE and the 
distance AF. Ans. FE 10.11 and AF 8.12. 










CHAP. IV. 


LAYING OUT AND DIVIDING LAND. 


197 


PROBLEM XIX. 

The boundaries of a tract of land ABCDEFGHIA, Fig. 
108 , being given , to divide it into two equal parts by a line 
IN running from the corner I and falling on the opposite 
side CD. 


RULE. 

Suppose lines drawn from I to C and D, and calcu¬ 
late the area of the whole tract. 

j£j I 4 

Take the corrected latitudes and departures* of IA, 
AB, and BC, and by balancing find the latitude and 
departure of Cl; also calculate the area of the part 
IABCI; from half the area of the whole tract, sub¬ 
tract the area of the part IABCI, the remainder will be 
the area of the triangle ICNI. 

Take the latitudes and departures of IC and CD, 
and by balancing find the latitude and departure of DI, 
and calculate the area of the triangle ICDI. Then, 

% v* 

As the area of the triangle ICDI, 

Is to the area of the triangle ICNI; 

So is the latitude of CD, 

To the latitude of CN. 

Also, As the area of the triangle ICDI, 

Is to the area of the triangle ICNI; 

So is the departure of CD, 

To the departure of CN. 


* It is the corrected latitudes and departures that are to be used 
throughout the calculation. 






198 


LAYING OUT AND DIVIDING LAND. 


CHAP. IV. 


Now take the latitudes and departures of IC and CN, 
and by balancing find the latitude and departure of the 
division line NI, with which find its bearing and dis¬ 
tance.* * • JJ 

EXAMPLES. 

* 

1. Let the bearing of AB be N. 19° E. dist. 27 ch. 
BC, S. 77° E. 22.75 ch. CD, S. 27° E. 28.75 ch. DE, S. 
52° W. 14.50 ch. EF, S. 15*° E. 19 ch. FG, West, 17.72 
ch. GH, N. 36° W. 11.75 ch. HI, North, 16.07 ch., and 
1A, N. 62° W. 14.88 ch.; it is required to divide the 
tract into two equal parts by a line IN running from 
the corner I and falling on the opposite side CD. 

First, calculate the whole area, thus: 


* This rule needs no demonstration. 




\ 












CHAP. IV. 


W 

c3 

CD 

<] 


m 

ci 

<l) 

c 


A 

+> *h 

3.2 

s*a 


P 

P 

£ 


Q 

P 

W 


W 


02 


Jh • 

O rj 

O 


Ott 


W 


02 


w 

o 

o 


GO 

Tp 


O 

eo 

CD 


LO 

d 

G< 


G* 

O 


C5 

l> 

co 


I GO 
LO 

*o 

G* 


P 


O 

o 

t~- 

G* 


to 

o 

to 

Si 

3 

o 

XJ 


d 

m 


m 

< 


tp 

I- 

GJ 

05 

CO 

>0 


H 

o 

05 


W 

CO 

05 

d 

co. 


LAYING OUT AND DIVIDING LAND. 

■',( , ■! 

jif •'•'« ;■ > • 

—* =—-- 


G^ 

t- 

GO 

r—i 

CO 

05 

CO 


CO 

CO 

GO 

05 

CO 

O 

CO 


H 

GO 

G< 

CO 

CO 


w 

05 

q 

d 

CO 


w 

lO 


CO 


05 

CO 

TP 


H 

LO 

05 

CO 

TP 


o 

o 

GO 

GJ 

H 

GO 

G2 


w 

Tp 

GO 

Tp 

G< 


o 

Tp 

G* 

o 

CO 

G4 


G^ 


GO 


rH 

o 

o 

t- 

CO 

CO 

LO 

05 

05 

q 

t- 

GO 

lM 

o 

LO 

tP 

LO 

G* 

LO 

o 

LO 


GO 

r—1 


O 

CO 


O 

GO 


t- 

‘O 

CO 

H 

tP 

SO 


W 

LO 

TP 


H 

GO 

GO 


CO 

05 

o 

GO 


LO 

G4 

LO 

GO 


G* 

GO 

d 


co 

CO 


CO 

lM 

g* 

G< 


GO 

lM 

LO 


t- 

o 

GO 


Tp 

CO 

LO 

G* 


Tp 


TP 

05 

00 


05 

o 

LO 


GJ 

GO 

CO 


G* 

CO 

G* 


CO 

Tp 

G* 


05 

CO 

CO 


t- 

r- 


i o 

05 
CO 


G* 

rH 

GO 


GO 

th 

GO 


' I 
O 


o 

>o 

05 


CO 

o 

CO 


t- 

05 

CO 


G$ 

O 


G* 

O 


G* 

TP 


G} 

G< 


I lo 

O 

GO 


GJ 

i—i 

LO 


G$ 

CO 

LO 

G* 


CO 

05 

CO 


CO 

o 

LO 


q 

co 


G* 

t- 


05 

d 


LO 

r- 

gI 

G* 


co 

G< 


o 

LO 

TP 


o 

o 

«• 

05 


G4 

t- 


TP 

tH 

GO 


LO 

05 


r- 

o 

d 


LO 

l- 


t- 

o 

d 


W 


t- 

m 


W 


i- 

G* 

Xfl 


G* 

LO 

U1 


W 

r*n 

LO 

rH 

m 


W 

<o 


co 

GO 


Si 

o 

£ 


O 

n 


p 

o 


H 

P 


P 

W 


O 

P 


a 

o 


05 

CO 

• 

t- 

co 


05 

CO 

co 


LO 

1—I 

• 

05 

TP 


LO 

05 

TP 


TP 

O 

CO 

LO 


Tp 

o 

00 

LO 


05 

o 

05 

tP 


CO 

05 

d 


CO 

CO 

TP 


G4 

Tp 

d 


G* 

CO 

S5 


G< 


05 

rH O 
05 d 

Tp Tp 


CO 

o> 

I> 
LO 


2 CG 

q 05 

CO 

Vi LO 


JO 

o 

6* 
w 

< 
t—< 

a 

o 

p 

w 

p 

XJ 

M 

<1 

Cm 

o 

d 

05 

< 


o 

05 

05 

CO 

G? 

CO 

t- 


o 4 


o 

T3 


O 

TO 


Cm 

3 

a 


w 

Si 

w 

o 


m 

U4 

H 


199 


/ 
















































































































































200 


LAYING OUT AND DIVIDING LAND. 


CHAP. IV. 


To find the latitude and departure of Cl, and area of the 

part IABCL 


Sta. 

N. 

S. 

E. 

W. 

E.D-D 

WDD 

Mult. 

N. A. 

S. Areas. 

i—i 

> 

6.97 



13.13 


30.98 

0.00 E 

—• 


AB 

25.51 


8.80 



4.33 

4.33 W 

-■ 

110.4583 

BC 


5.13 

22.18 


30.98 


26.65E 

* f 

136.7145 

Cl 


(27.35) 


(17-85) 

4.33 


30.98E 


847.3030 


32.48 

32.48 

30.98 

30.98 

35.31 

35.31 



1094.4758 


Area of IABCI (sq. ch.) 547.2379 

Half area of ABCDEFGIIIA 762.6990 


Area of ICNI (sq. ch.) 215.4611 


To find the area of ICDI. 


Sta. 

N. 

S. 

E. 

W. 

E-D.D 

WDD 

Mult. 

N. A. 

S. Areas. 

IC 

27.35 


17.85 



13.07 

0.00E 



CD 


25.64 

13.07 


30.92 


30.92E 


792.7888 

DI 


(1.71) 


(30-92) 


17.85 

13.07E 


22.3497 


27.35 

27.35 

30.92 

30.92 

30.92 

30.92 



815.1385 


Area of ICDI (sq. ch.) 407.5692 


As area of ICDI 407.57 

: area of ICNI 215.46 - 

: : latitude of CD 25.64 S. 

: latitude of CN 13.55 S. 


Ar. Co. 7.38980 
2.33337 
1.40892 


1.13209 


As area of ICDI 407.57 

: area of ICNI 215.46 

: : departure of CD 13.07 E. 


Ar. Co. 7.38980 
2.33337 

% 

1.11628 


: departure of CN 0.91 E. - - 0.83915 























































































































CHAP. IV. 


LAYING OUT AND DIVIDING LAND. 


201 


To find the latitude and departure of NI. 


Sta. 

N. 

S. 

E. 

W. 

IC 

27.35 


17.85 


CN 


13.55 

6.91 


NI 


(13.80) 


24.76 


27.35 

27.35 

24.76 

24.76 


» 

To find the hearing and distance of NI. 


As diff. of lat. of NI, 13.80 S. 

: dep. do. 24.76 W. 

:: rad. - 


Ar. Co. 8.86012 
1.39375 
10.00000 


: tang, bearing of NI, S. 60° 52' W. - 10.25387 


As rad. - 
: sec. bearing of NI, 60° 52' 
: : diff. lat. do. 13.80 


Ar.-Co. 0.00000 
10.31261 
1.13988 


: dist. NI, 28.35 ch. - 1.45249 

Hence IN bears, N. 60° 52' E. dist. 28.35 ch. 


2. Given the boundaries of a tract of land as follow: 
viz. 1st. S. 35i° W. 11.20 ch.; 2nd. N. 45° W. 24.36 ch.; 
3rd. N. 15£° E. 10.80 ch; 4th. S. 77° E. 16 ch.; 5th. N. 
87£° E. 21.50 ch ; 6th. S. 60° E. 14.80 ch.; 7th. South, 
10.91 ch.; 8th. N. 85° W. 29.28 ch. to the place of be¬ 
ginning; to divide the tract into two equal parts by a 
line running from the first station and falling on one of 
the opposite sides ; the bearing and distance of the di¬ 
vision line are required. Jins. N. 7° 18' E. 15.28 ch. 

C c 































CHAPTER V. 




VARIATION OF THE COMPASS. 


A meridian pointed out by the magnetic needle is 
not in general a true one; for the needle does not point 
truly to. the north point of the horizon, but varies from 
it, in some places to the eastward, and in others to the 
westward. 

The angle contained between the true meridian and 
that pointed out by the needle, is called the variation of 
the compass. 

The variation is named east or west , according as the 
needle points to the eastward or westward of the true 
north. 

As the variation is different in different places, so also 
in the same place it does not remain the same, but 
differs sensibly in the course of a few years. Hence 
in running a line that was run a number of years pre¬ 
viously, the bearing will be found different from what it 
was at that time; this, together with the difference in 
compasses, causes many difficulties, and frequently in¬ 
accuracies, in tracing old lines. 


t 


I 


€HAP. V. VARIATION OP THE COMPASS. 203 

The easiest way to guard against those difficulties 
and inaccuracies would be to make and return the sur¬ 
veys according to the true, and not the magnetic, bear¬ 
ings. In order to do this it will be necessary to know 
the variation of the compass for the place in which the 
survey is made; and this may readily be found by first 
tracing a meridian line in the following manner. 

To draw a true meridian line by means of the greatest elon¬ 
gation of the pole star. 

The pole star is situated about 1° 41' from the true 
pole, and therefore apparently revolves round it, in a 
small circle, once in about 23 h. 56 m. When at its 
greatest distance east or west from the true pole, it is 
said to be at its greatest east or west elongation. It 
is therefore evident that in the course of one apparent 
revolution it must be twice at its greatest elongation, 
once to the east and once to the west. 

The following tables exhibit the times, nearly, of the 
greatest eastern elongations of the pole star for six 
months of the year, and of the greatest western elonga¬ 
tions for the other six months. The other greatest elon¬ 
gations take place in the day time, and are therefore 
invisible. Some of those inserted in the tables are 
also invisible; because they occur, either before day¬ 
light is gone in the evening, or after it has returned in 
the morning. The most of those in the 3rd, 4th, 9jth 
and 10th months are in this situation. 

The time in the tables is reckoned from noon, and 
therefore when it is less than 12 hours, the greatest 
elongation takes place in the evening of the same day; 
but when it exceeds 12 hours, if 12 hours be subtracted 
from it, the remainder will be the time of greatest elon¬ 
gation in the morning of the following day. 


204 


VARIATION OF THE COMPASS. 


CHAP. V. 


Eastern Elongation, 


Days- 

4mo.(Ap.) 

5mo.(Ma.) 

6mo.(Ju.) 

7mo.(July.) 

8mo-(Aug.) 

9mo.(Sep.) 


H. 

M. 

H. 

M. 

H. 

M. 

H. 

M. 

H. 

M. 

H. 

M. 

1 

18 

18 

16 

26 

14 

24 

12 

20 

10 

16 

8 

20 

7 

17 

56 

16 

3 

14 

0 

11 

55 

9 

53 

7 

58 

13 

17 

34 

15 

40 

13 

35 

11 

31 

9 

30 

7 

36 

19 

17 

12 

15 

17 

13 

10 

11 

7 

9 

8 

7 

15 

25 

16 

49 

14 

53 

12 

45 

10 

43 

8 

45 

6 

53 


Western Elongation, 


Days- 

lOmo. 

(Oc.) 

llmo. 

(No.) 

12mo 

.(Do.) 

lmo. 

(Ja.) 

2mo.(Feb.) 

3mo.(Mar-)i 


H. 

M. 

H. 

M. 

H. 

M. 

H. 

M. 

H. 

M. 

H. 

M. 

1 

18 

18 

16 

22 

14 

19 

12 

2 

9 

50 

8 

1 

7 

17 

56 

15 

59 

13 

53 

11 

36 

9 

26 

7 

38 

13 

17 

34 

15 

35 

13 

27 

11 

10 

9 

2 

7 

16 

19 

17 

12 

15 

10 

13 

00 

10 

44 

8 

39 

6 

54 

25 

16 

49 

14 

45 

12 

34 

10 

18 

8 

16 

6 

33 


To find the angle of bearing, or azimuth of the pole 
star, when at its greatest elongation ; subtract its decli¬ 
nation from 90°, and the remainder will be the polar 
distance. Then, 

As radius, 

Is to the secant of the latitude; 

So is the sine of the polar distance, 

To the sine of the azimuth. 

The mean declination of the pole star of the 1st of the 
first month (January) 1820, was 88° 20' 55" N.; and it 
increases 19.4" yearly; hence the mean declination 
may readily be obtained for any given time. 

When great accuracy is required, the mean declina¬ 
tions must be corrected by allowing for aberration and 
nutation; but as these corrections are small, they are 
not necessary when our object is only to determine the 
variation of the compass.. 


































CHAP. V 


VARIATION OF THE COMPASS. 


205 


The following table exhibits the angle of bearing, 
or azimuth of the pole-star, when at its greatest elon¬ 
gation; calculated to the 1st of the first month (Janu¬ 
ary) and of the seventh month (July), for each of the 
years contained in the first column, and for the differ¬ 
ent degrees of north latitude at the head of the table. 
In calculating it, the star’s mean de clination was cor¬ 
rected, by allowing for aberration and nutation. 




Lat. 36° 

Lat. 

38° 

Lat. 

40° 

Lat. 42° 


Lat. 

44° 

Years 

Months. 

Azimuth. 

Azimuth. 

Azimuth. 

Azimuth. 

Azimuth. 

1824 

1 mo. 1 

2 ( 

3 0' 

21" 

G}0 

*** 

3' 

32" 

2° 

7' 

4' 

2‘ 

3 10 7 59" 

2° 15' 

20" 

7 mo. 1 

2 

0 

57 

2 

4 

11 

2 

7 

45 

2 

11 

41 

2 

16 

3 

1825 

1 mo. 1 

1 

59 

59 

2 

3 

9 

2 

6 

41 

2 

10 

35 

2 

14 

55 

7 mo. 1 

2 

0 

35 

2 

3 

48 

2 

7 

21 

2 

11 

17 

2 

15 

38 

1826 

1 mo. 1 

1 

59 

36 

2 

2 

46 

2 

6 

17 

2 

10 

11 

2 

14 

30 

7 mo. 1 

2 

0 

13 

2 

3 

25 

2 

6 

58 

2 

10 

53 

k 

15 

13 

1827 

1 mo. 1 

1 

59 

14 

2 

2 

24 

2 

5 

54 

2 

9 

47 

2 

14 

5 

7 mo. 1 

1 

59 

50 

2 

3 

3 

2 

6 

34 

2 

10 

28 

2 

14 

48 

1828 

1 mo. 1 

1 

58 

52 

2 

2 

1 

2 

5 

31 

2 

9 

23 

2 

13 

40 

7 mo. 1 

1 

59 

28 

2 

2 

40 

2 

6 

11 

2 

10 

4 

2 

14 

23 

1829 

1 mo. 1 

1 

58 

29 

2 

1 

38 

2 

5 

7 

2 

8 

58 

2 

13 

15 

7 mo. 1 

1 

59 

6 

2 

2 

17 

2 

5 

47 

2 

9 

40 

2 

13 

58 

1830 

1 mo. 1 

1 

58 

7 

2 

1 

15 

2 

4 

44 

2 

8 

34 

2 

12 

51 

7 mo. 1 

1 

58 

44 

2 

1 

54 

2 

5 

24 

2 

9 

16 

2 

13 

33 

1831 

1 mo. 1 

1 

57 

45 

2 

0 

52 

2 

4 

21 

2 

8 

10 

2 

12 

26 

7 mo. 1 

1 

58 

22 

2 

1 

31 

«» 

2 

5 

0 

2 

8 

52 

2 

13 

8 

1832 

1 mo. 1 

1 

57 

23 

2 

0 

30 

2 

3 

58 

2 

7 

46 

2 

12 

1 

7 mo. 1 

1 

57 

59 

2 

1 

9 

2 

4 

37 

2 

8 

27 

2 

12 

43 

1833 

1 mo. 1 

1 

57 

0 

2 

0 

7 

2 

3 

44 

2 

7 

22 

2 

11 

36 

7 mo. 1 

1 

57 

37 

2 

0 

46 

2 

4 

13 

2 

8 

3 

2 

12 

18 

1834 

1 mo. 1 

1 

56 

38 

1 

59 

44 

2 

3 

11 

2 

6 

58 

2 

11 

11 

7 mo. 1 

1 

57 

15 

2 

0 

23 

2 

3 

50 

2 

7 

39 

2 

11 

53 





















































































206 


VARIATION OF THE COMPASS. 


CHAP. V. 


Note .—The azimuths in the foregoing table corres¬ 
ponding to the 1st of the first month (January) of each 
year, are easterly , and those corresponding to the 1st 
of the seventh month (July) are westerly. 

In order to observe the greatest elongation of the 
pole star, it will be necessary to prepare the following 
simple apparatus. 

i 

Place two posts firmly in the ground, about three feet 
apart, and nearly east and west from each other; the 
heights of the posts, which should be the same, may 
be about two or three feet; on those posts, place a thick 
board or plank, five or six inches wide, and nail it fast 
to each of them, taking care that it be level or nearly 
so : take a piece of board, a foot or eighteen inches 
long and four or five wide, and near the middle of it 
fasten a compass-sight perpendicularly ; this board is 
to slide on the horizontal one already mentioned. 

Take a stiff pole 18 or 20 feet in length, and fix it in 
an inclined position, in such a manner that a plumb line 
suspended from the upper end, may be nearly north, 
and about ten feet distant, from the middle of the hori¬ 
zontal board; the elevation of the pole must be such 
that the pole star, when viewed through the compass- 
sight placed on the horizontal board, may appear a 
few inches below its upper end; when in this position 
the lower end should be fastened in the ground, and the 
pole should be supported by a couple of crotchets placed 
near the middle. The plumb should weigh a pound 
or more, and should swing in a vessel of water, in order 
to prevent the line being agitated by the motion of the 
air. 

The apparatus being prepared, proceed, about 15 or 
20 minutes previous to the time of greatest elongation 


CHAP. V. 


VARIATION OF THE COMPASS. 


207 


as indicated by the table, to make the observation as 
follows: Let an assistant hold a lighted candle near 
the plumb line, so as to illuminate it and render it dis¬ 
tinctly visible; place the small board with the compass- 
sight attached to it, on the horizontal one, and move it 
east or west as the case may require, till the pole star, 
plumb-line, and aperture in the compass-sight are all in 
a direct range. If the star should be deviating to the 
east, it will leave the plumb-line to the west; and the 
contrary if deviating to the west; keep therefore shift¬ 
ing the sight, till the star appears stationary behind the 
plumb-line ; which it will do for several minutes at the 
time of its greatest elongation, and will then recede 
from the line on the contrary side from which it did be¬ 
fore it became stationary. The compass-sight must 
not be moved after the star has attained its greatest 
elongation; but the aperture in it being then in a direct 
range with the plumb-line and star, the board to which 
the sight is fixed, must be fastened to the one on which 
it slides, by a small tack passing through each end. 
This being done let an assistant take a straight stake, 
with a piece of lighted candle stuck on it, and go north 
to the distance of 30 or 40 perches; then looking 
through the compass-sight, direct him to set it up per- 

« 

pendicularly, and in such a situation that the candle 
stuck on the top may appear exactly behind the plumb- 
line; when thus placed, let it be firmly fixed in the ground, 
next let another straight stake be set up in the same 
manner near the plumb-line; the remaining part of the 
work may then be left till morning. 

Measure accurately the distance between the two 
stakes; and from the table of azimuths take out, for 
the given time and latitude, the azimuth of the pole 
star when at its greatest elongation. This azimuth 


208 


VARIATION OF THE COMPASS. 


CHAP. V. 


will be west if the time is within two months, before or 
after the 1st of the first month (January,) but east if 
within the like time of the 1st of the seventh month 
(July.) Then, 

As radius, 

Is to the tangent of the azimuth ; 

So is the distance between the stakes in feet, 

To a fourth term in feet. 

Lay off the number of feet contained in this fourth 
term from the northerly stake, and perpendicular to a 
line joining the two stakes; it must be laid off towards 
the west if the azimuth is east , but towards the east if the 
azimuth is west. Next remove the northerly stake, and 
set it up at the other extremity of the distance thus laid 
off; then a straight line joining the two stakes will be 
a true meridian line. 

To obtain the variation, set up a compass in the 
place of the southerly stake, and direct the sights truly 
to the northerly one ; the needle will then point out the 
variation, which will be east or west , according as the 
needle points to the east or west of the north point of 
the compass. The whole process is so simple, that an 
example is deemed unnecessary. 

It has already been observed, that the greatest elonga¬ 
tions of the pole star are invisible during the greater 
part of the 3rd. and 4th months, and also of the 9th and 
10th ; consequently a meridian line cannot be obtained 
by the preceding method, during those periods. But as 
the surveyor may generally choose his time for tracing a 
meridian line, and as, when this is done, he can at any 
time obtain the variation, it is thought unnecessary to 
introduce other methods. Those, however, who would 
wish to be acquainted with simple and accurate methods 
of tracing a meridian line at any season of the year, may 


€HA 1*. V. VARIATION OF THE COMPASS. 209 

consult a pamphlet on the subject, by .Andrew Elicott , 
A. M. from which the substance of the preceding me¬ 
thod is extracted, and which contains others suited to 
those times of the year in which this cannot be applied. 
It may not be improper also to observe, that the second 
volume of the American Philosophical Transactions con¬ 
tains an essay by Robert Patterson , Professor of Mathe¬ 
matics in the University of Pennsylvania, in which is given 
a method for obtaining the variation to a sufficient de¬ 
gree of accuracy for any purpose in surveying, and 
which has this advantage, that the observation may be 
made at any season of the year, and at any time in the 
evening. There are also other methods besides those 
alluded to above, by which a meridian line may be 
traced, or the variation of the compass determined: 
but as the most of them require expensive intruments 
for making the observation, it is thought unnecessary 
to notice them in this work. 

To obtain the true bearings of ci survey,from the magnetic 
ones , the variation being given. 

If the variation be east , add it to the north-easterly 
and south-westerly bearings, and subtract it from those 
that are north-westerly or south-easterly; but if the 
variation be ivest , add it to the north-westerly and south¬ 
easterly bearings, and subtract it from those that are 
north-easterly or south-westerly ; this being done, the 
true bearings are obtained. 

To find the difference betiocen the present variation , and that 
at a time when a tract of land ivas formerly surveyed , in 
order to trace or run out the original lines. 

Go to any part of the premises, where any two adja¬ 
cent corners are known; and if one can be seen from 
Dd 


210 


VARIATION OF THE COMPASS. 


CHAP. V. 


the other, take their bearing; which compared with 
that of the same line in the former survey, shows their 
difference. But if one corner cannot be seen from the 
other, run the line according to the given bearing, and 
measure the nearest distance between the line so run 
and the corner; then, 

# 

As the length of the given line, 

Is to the said distance; 

So is 57.3 degrees,* 

To the difference of variation required. 

EXAMPLES. 

* « % 

Suppose it be required to run a line, which some 
years ago bore N. 45° E. dist. 20 ch. and in running 
this line by the given bearing, the corner is found 20 
links to the left hand; what allowance must be made 

on each bearing to trace the old lines, and what is the 

« 

present bearing, by the compass, of this particular line ? 

L. L. Deg. 

As 2000 : 20 :: 57.3 

20 

2000)1146.0(0° 34' rib. 

Consequently 34 minutes, or little more than half a 
degree, is the allowance required, and the line in ques¬ 
tion bears N. 44° 26' E. 

Note. The above rule is simple and sufficiently ac¬ 
curate when the distance between the sought corner and 


* 57.3 is the radius (nearly) of a circle in such parts as the circum¬ 
ference contains 360. 





CHAP. V. 


VARIATION OF THE COMPASS. 


211 


random line, is small. But when this distance is consi¬ 
derable, it will be better to find the angle by trigono¬ 
metry. 


ON LOCAL ATTRACTION. 

It is well known that iron or any ferruginous sub¬ 
stance attracts the magnetic needle, and consequently 
when near will draw it aside from the position in which 
it would otherwise settle. And as the earth in many 
places contains, near its surface, substances of this kind, 
the needle will not unfrequently be attracted from its 
true direction. The surveyor ought therefore, at each 
station, to take a back view to the preceding one; and 
if he arrive at one at which the compass does not re¬ 
verse truly, he may conclude, provided no error was com¬ 
mitted in taking the bearing at the last station, that at 
the present one, the needle is affected by some local at¬ 
traction. In such a case, he should first determine 
whether any error was committed at the last station, 
and if none is found, take the difference between the 
bearing from the last station and the reverse bearing, 
which will be the local variation of the needle at the 
present station. This variation must be applied accor¬ 
ding to its name, to the bearing of the following station. 

If at the first and second station of a survey the 
compass is found not to reverse truly, the surveyor will 
be at loss to know which of them is affected by attrac¬ 
tion. But by taking another station, either within or 
without the survey, and taking its bearing from each of 






212 VARIATION OF THE COMPASS. CHAP. V. 

those stations, and the bearing of each of those from 
it, he may in general determine, at which of them 
the attraction exists. 

Note. The area of the survey is not affected by the 
general variation, because it is the same at each sta¬ 
tion. But where local attraction exists and causes a 
variation in the position of the needle, as this variation 
will be different at different stations, it will, unless ascer¬ 
tained, and allowed on the corresponding bearings, 
materially affect the truth of the survey. 












i 










CHAPTER VI. 


MISCELLANEOUS QUESTIONS. 

1. A circular fish-pond is to be dug in a garden, that 
shall take up just half an acre: what must be the 
length of the cord that strikes the circle ? 

Arts. 27.75 yards. 

2. Two sides of a triangle are 20 and 40 perches re¬ 
spectively : required the third side, so that the content 
may be just an acre. 

Am. Either 23.099 or 58.876 perches. 

3. In 110 acres of statute measure, in which the pole 
is 5.5 yards, how many Cheshire acres, where the cus¬ 
tomary pole is 6 yards, and how many of Ireland where 
the pole in use is 7 yards ? 

Am. 92 A. 1 R. 29 P. Cheshire; 67 A. 3 R. 25 P. Irish. 

4. The ellipse in Grosvenor square, London, mea- 
sures 840 links the longer way, and 612 the shorter, 
within the rails; now the wall being 14 inches thick, it 
is required to find what quantity of ground it encloses, 
and how much it stands upon. 

A ns. It encloses 4 A. 0 R. 6 P. and stands on 1760 a 
square feet. 

5. Required the dimensions of an elliptical acre, with 
the greater and less diameters in the ratio of 3 to 2. 

A ns. 17.481 by 11.654 perches. 





214 MISCELLANEOUS QUESTIONS. CHAP. VI. 

6. The three sides of a triangular field, containing 
0 A. 1 R. 12 P. are in the ratio of the three numbers, 

9, 8, G, respectively; required the sides. 

Ans . 59.029, 52.47, and 39.353 perches. 

7. In a pentangular field, beginning with the south 
side and measuring round towards the east, the first or 
south side is 27.35 ch., the second 31.15 ch., the third 
23.70 ch., the fourth 29.25 ch., and the fifth 22.20 ch.; 
also the diagonal from the first angle to the third is 38 
ch., and that from the third to the fifth 40.10 ch.; re¬ 
quired the area of the field. Arts, 117 A. 2 R. 39 P. 

8. Required the dimensions of an oblong garden, con¬ 
taining three acres, and bounded by 104 perches of pale 

fence.* - Jins. 40 perches by 12. 

* 

9. How many acres are contained in a square mea¬ 

dow, the diagonal of which is 20 perches longer than 
either of its sides? A ns. 14 A. 2 R. 11 P. 

10. A gentleman has a garden 100 feet long and 80 
broad, and a gravel walk is to be made of equal width 
half round it; what must be the width of the walk, so 
that it may take up just one-fourth of the ground ? 

* Ans. 11.8975 feet. ^ 

11. A person has a circular yard that is 150 feet in 
diameter, and wishes a walk of equal width made 
round it within the fence : required the width of the 
walk, so that it may occupy a fifth part of the ground. 

Ans. 7.918 feet. 


* This question may be neatly constructed by 28, C Playfair''s 
Geometry. It may not be improper also to observe, that the 2nd 
question, and all those following the 8th, admit of neat geometrical 
constructions. * *' 






CHAP. VI. MISCELLANEOUS QUESTIONS. 215 

I 

12. From a point within a triangular field, the sides 
of which were .equal, 1 measured the distances to the 
three angles, and found them 12.5, 10, and 7.5 chains, 
respectively; required the area. Am. 12 A. 1 R. 22 P. — 

13. On examining the field-notes of a lot of ground 
of which I wished to know the content, I found them 
as follow: 1st. S. 72° W. 24 per., 2nd. North, 38 per., 

3rd, N. 82 h E. 41 per., 4th.--, 20 per., 5th. S. 80° E. 

11.5 per., 6th. S. 26° W. 22 per., and 7th.-, 37 per., 

to the place of beginning. The bearings of the 4th 
and 7th boundary lines were illegible; but the data re¬ 
maining being sufficient, the area is required. 

Ans. 12 A. 3 R. 2 P. 

14. It is required to lay out 4^ acres of land in a tri- 
angular form, so that the length of one side may be 
15 chains, and the lengths of the other sides in the ratio 
of 2 to 3; what must be the lengths of those sides ? 

Am. 7.7914 and 11.6871 chains; or 29.58536 and 
44.37804 chains. 

15. It is required to lay out five acres of ground in a 
triangular form to be bounded by 135 perches of fence; 
the length of one side is to be 50 perches; what must 
be the lengths of the other sides ? 

Am. 33.3785 and 51.6215 perches. 

16. The area of a rectangular field is 7i acres, and 

the length of the diagonal 50 perches: required the 
sides. Am. 30 and 40 perches, , 

17. In a rectangular tract of land, containing 58 A. 

3 R. 8 P. the difference of the lengths of the sides is just 
equal to the difference between the lengths of the 
longer side and the diagonal; hence the sides are re¬ 
quired. Am. 21 and 28 chains. 








216 MISCELLANEOUS QUESTIONS. CHAP. VI. 

18. The boundaries of a tract of land are as follow : 
1st. N. 14° W. 15.20 ch.: 2nd. N. 70£° E. 20.43 ch. ; 
3rd. S. 6° E. 22.79 ch.; 4th. N. 86?° W. 18 to the place 
of beginning; within the tract there is a spring, the 
bearing and distance of which, from the 2nd corner, is 
S. 75° E. 7;90 ch. It is required to cut off 10 acres 
from the west side of this tract by a straight line run¬ 
ning through the spring; what must be the distance of 
the division line from the 1st corner, measured on the 

fourth side ? Ans. 4.6357 chains. 

. ^ 

19. The boundaries of a quadrilateral tract of land 
are as follow: 1st N. 35±° E. 23 ch. ; 2nd. N. 75i° E. 
30.50 ch.; 3rd. S. 3^° E. 46.49 ch. and 4th. N. 66^° W. 
49.64 ch., to the place of beginning. This tract is to 
be divided into four equal parts by two straight lines, 
one of which is to run parallel to the 3rd side; re¬ 
quired the distance of the parallel division line from 
the first comer, measured on the 4th side; also the 
bearing of the other division line and its distance from 
the same corner, measured on the 1st side. 

Ans. Distance of the parallel division from the first 
corner 32.50 chains, the bearing of the other, S. 88° 
22' E. and its distance from the same corner 6 chains. 



FINIS. 


MATHEMATICAL TABLES: 

DIFFERENCE 


OF 

LATITUDE AND DEPARTURE; 


LOGARITHMS, 


PROM 1 TO 10,000; 


AND 


ARTIFICIAL SINES, TANGENTS, AND 

SECANTS. 




STEREOTYPE EDITION, CAREFULLY REVISED AND CORRECTED. 


PuiaMiJiua: 

PUBLISHED BY KIMBER AND SHARPLESS, 

NO. 8, S. FOURTH-STREET. 

1829. 


Stereotyped by J. Howe, New-York. 

L ' 





2 


TRAVERSE TABLE 


Distance. 

) 

i Deg. 

. 

£ Deg. 

1 Deg. 

Distance. 

Lat. | 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

1 

1.00 

0.00 

1.00 

0.01 

1.00 

0.01 

1 

2 

2.00 

0.01 

2.00 

0.02 

2.00 

0.03 

2 

3 

3.00 

0.01 

3.00 

0.03 

3.00 

0.04 

3 

4 

4.00 

0.02 

4.00 

0.03 

4.00 

0.05 

4 

5 

5.00 

0.02 

5.00 

0.04 

5.00 

0.07 

5 

6 

6.00 

0.03 

6.00 

0.05 

6.00 

0.08 

6 

7 

7.00 

0.03 

7.00 

0.06 

7.00 

0.09 

7 

8 

8.00 

0.03 

8.00 

0.07 

8.00 

0.10 

8 

9 

9.00 

0.04 

' 9.00 

0.08 

9.00 

0.12 

9 

10 

10.00 

0.04 

10.00 

0.09 

10.00 

0.13 

10 

11 

11.00 

0.05 

11.00 

0.10 

11.00 

1 0.14 

11 

12 

12.00 

0.05 

12.00 

0.10 

12.00 

0.16 

12 

13 

13.00 

0.06 

13.00 

0.11 

13.00 

0.17 

13 

14 

14.00 

0.06 

14.00 

0.12 

14.00 

0.18 

14 

15 

15.00 

0.07 

15.00 

0.13 

15.00 

0.20 

15 

16 

16.00 

0.07 

16.00 

0.14 

16.00 

0.21 

16 

17 

17.00 

0.07 

17.00 

0.15 

17.00 

0.22 

17 

18 

18.00 

0.08 

18.00 

0.16 

18.00 

0.24 

18 

19 

19.00 

0.08 

19.00 

0.17 

19.00 

0.25 

19 

20 

20.00 

0.09 

20.00 

0.17 

20.00 

0.26 

20 ; 

21 

21.00 

0.09 

21.00 

0.18 

21.00 

0.27 

21 

22 

22.00 

0.10 

22.00 

0.19 

22.00 

0.29 

22 

23 

23.00 

0.10 

23.00 

0.20 

23.00 

0.30 

23 

24 

24.00 

0.10 

24.00 

0.21 

24.00 

0.31 

24 

25 

25.00 

0.11 

25.00 

0.22 

25.00 

0.33 

25 

26 

26.00 

0.11 

26.00 

0.23 

26.00 

0.34 

26 

27 

27.00 

0.12 

27.00 

0.24 

27.00 

0.35 

27 

28 

28.00 

0.12 

28.00 

0.24 

28.00 

0.37 

28 

29 

29.00 

0.13 

29.00 

0.25 

29.00 

0.38 

29 

30 

30.00 

0.13 

30.00 

0.26 

30.J00 

Q.89 

; 30 

31 

31.00 

0.14 

31.00 

0.27 

31.00 

0.41 

31 

32 

32.00 

0.14 

32.00 

0.28 

32.00 

0.42 

32 

; 33 

33.00 

0.14 

33.00 

0.29 

33.00 

0.43 

33 

34 

34.00 

0.15 

34.00 

0.30 

34.00 

0.45 

34 

35 

35.00 

0.15 

35.00 

0.31 

35.00 

0.46 

35 

36 

36.00 

0.16 

36.00 

0.31 

36.00 

0.47 

36 

37 

37.00 

0.16 

37.00 

0.32 

37.00 

0.48 

37 

38 

38.00 

0.17 

38.00 

0.33 

38.00 

0.50 

38 

39 

39.00 

0.17 

39.00 

0.34 

39.00 

0.51 

39 

40 

40.00 

0.17 

40.00 

0.35 

40.00 

0.52 

40 

41 

41.00 

0.18 

41.00 

0.36 

41.00 

0.54 

41 

42 

42.00 

0.18 

42.00 

0.37 

42.00 

0.55 

42 

: 43 

43.00 

0.19 

43.00 

0.38 

43.00 

0.56 

43 

44 

44.00 

0.19 

44.00 

0.38 

44.00 

0.58 

44 

45 

45.00 

0.20 

45.00 

0.39 

45.00 

0.59 

45 

46 

46.00 

0.20 

46.00 

0.40 

46.00 

0.60 

46 

\ 47 

47.00 

0.21 

47.00 

0.41 

47.00 

0.62 

47 

48 

48.00 

0.21 

48 * 00 

0.42 

48.00 

0.63 

48 

49 

49.00 

0.21 

49.00 

0.43 

49.00 

0.64 

49 

50 

50.00 

0.22 

50.00 

0.44 

50.00 

0.65 

50 

Distance. 

Dep. 

Lat. 

Dep; 

Lat. 

Dep. 

Lat. 

Distance. 

89J Deg. 

_ 

89£ Deg. 

89^ Deg. 










































































TRAVERSE TABLE 


3 


M 




1 

tT\ 



d 

• 

c/> 

\ Deg. 

h Deg. 

| Deg. 

O 

•— • 

c+- 

p 







§ 

p 







O 

? 

Lat. 1 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

o 

a 

• 

51 

51.00 

0.22 

51.00 

0.45 

51.00 

0.67 

51 

52 

52.00 

0.23 

52.00 

0.45 

52.00 

0.68 

52 

53 

53.00 

0.23 

53.00 

0.46 

53.00 

0.69 

53 

54 

54.00 

0.24 

54.00 

0.47 

54.00 

0.71 

54 

55 

55.00 

0.24 

55.00 

0.48 

55.00 

0.72 

55 

56 

56.00 

0.24 

56.00 

0.49 

56.00 

0.73 

56 

57 

57.00 

0.25 

57.00 

0.50 

57.00 

0.75 

57 

58 

58.00 

0.25 

58.00 

0.51 

57.99 

0.76 

58 

59 

59.00 

0.26 

59.00 

0.51 

58.99 

0.77 

59 

60 

60.00 

0.26 

60.00 

0.52 

59.99 

0.79 

60 

61 

61.00 

0.27 

61.00 

0.53 

60.99 

0.80 

61 

62 

62.00 

0.27 

62.00 

0.54 

61.99 

0.81 

62 

63 

63.00 

0.27 

63.00 

0.55 

62.99 

0.82 

63 * 

64 

64.00 

0.28 

64.00 

0.56 

63.99 

0.84 

64 

65 

65.00 

0.28 

65.00 

0.57 

64.99 

0.85 

65 

66 

66.00 

0.29 

66.00 

0.58 

65.99 

0.86 

66 

67 

67.00 

0.29 

67.00 

0.58 

66.99 

0.88 

67 

68 

68.00 

0.30 

68.00 

0.59 

67.99 

0.89 

68 

69 

69.00 

0.30 

69.00 

0.60 

68.99 

0.90 

69 

70 

70.00 

0.31 

70.00 

0.61 

69.99 

0.92 

70 

71 

71.00 

0.31 

71.00 

1 

0.62 

70.99 

0.93 

71 

72 

72.00 

0.31 

72.00 

0.63 

71.99 

0.94 

72 

73 

73.00 

0.32 

73.00 

0.64 

72.99 

0.96 

73 

| 74 

74.00 

0.32 

74.00 

0.65 

73.99 

0.97 

74 

75 

75.00 

0.33 

75.00 

0.65 

74.99 

0.98 

75 

76 

76.00 

0.33 

76.00 

0.66 

75.99 

0.99 

76 

77 

77.00 

0.34 

77.00 

0.67 

76.99 

1.01 

77 

78 

78.00 

0.34 

78.00 

0.68 

77.99 

1.02 

78 

79 

79.00 

0.34 

79.00 

0.69 

78.99 

1.03 

79 

80 

80.00 

0.35 

80.00 

0.70 

79.99 

1.05 

80 

01 

81.00 

0.35 

81.00 

0.71 

80.99 

1.06 

81 

82 

82.00 

0.36 

82.00 

0.72 

81.99 

1.07 

82 

83 

83.00 

0.36 

83.00 

0.72 

82.99 

1.09 

83 

84 

84.00 

0.37 

84.00 

0.73 

83.99 

1.10 

84 

85 

85.00 

0.37 

85.00 

0.74 

84.99 

1.11 

85 

86 

86.00 

0.38 

86.00 

0.75 

85.99 

1.13 

86 

87 

87.00 

0.38 

87.00 

0.76 

86.99 

1.14 

87 

88 

88.00 

0.38 

88.00 

0.77 

87.99 

1.15 

88 

89 

89.00 

0.39 

89.00 

0.78 

88.99 

1.16 

89 

90 

90.00 

0.39 

90.00 

0.79 

89.99 

1.18 

90 

1 91 

91.00 

0.40 

91.00 

0.79 

90.99 

1.19 

91 

| 92 

92.00 

0.40 

92.00 

0.80 

91.99 

1.20 

92 

I 93 

93.00 

0.41 

93.00 

0.81 

92.99 

1.22 

93 

I 94 

94.00 

0.41 

94.00 

0.82 

93.99 

1.23 

94 

> 95 

95.00 

0.41 

95.00 

0.83 

94.99 

1.24 

95 

I 96 

96.00 

0.42 

96.00 

0.84 

95.99 

1.26 

96 

97 

97.00 

0.42 

97.00 

0.85 

96.99 

1.27 

97 

98 

98.00 

0.43 

98.00 

0.86 

97.99 

1.28 

98 

; 99 

99.00 

0.43 

99.00 

0.86 

98.99 

1.30 

99 

100 

100.00 

0.44 

100.00 

0.87 

99.99 

1.31 

100 

1 4) 

1 o 

Dep. 

1 Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

m 

CD 

O 

c 

1 a 

1 -*-» 

1 ,ri 

1 Q 

89| Deg. 

89£ Deg. 

89} Deg. 

a 

•M 

DO 
* H 

Q 


\ 

















































































4 


TRAVERSE TABLE 


d 

H* ♦ 

w 

rt* 

fO 

1 Deg. 

H Deg. 

H Deg. 

Deg. 

d 

. 

OD 

P 

P 

3 

o 

fl> 

• 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

o 

• 

1 

1.00 

0.02 

1.00 

0.02 

1.00 

0.03 

1.00 

0.03 

1 

2 

2.00 

0.03 

2.00 

0.04 

2.00 

0.05 

2.00 

0.06 

2 

3 

3.00 

0.05 

3.00 

0.07 

3.00 

0.08 

3.00 

0.09 

3 

4 

4.00 

0.07 

4.00 

0.09 

4.00 

0.10 

4.00 

0.12 

4 

5 

5.00 

0.09 

5.00 

0.11 

5.00 

0.13 

5.00 

0.15 

5 

6 

6.00 

0.10 

6.00 

0.13 

6.00 

0.16 

6.00 

0.18 

6 

7 

7.00 

0.12 

7.00 

0.15 

7.00 

0.18 

7.00 

0.21 

7 

8 

8.00 

0.14 

8.00 

0.17 

8.00 

0.21 

8.00 

0.25 

8 

9 

9.00 

0.16 

9.00 

0.20 

9.00 

0.24 

9.00 

0.28 

9 

10 

10.00 

0.17 

10.00 

0.22 

10.00 

0.26 

10.00 

0.31 

10 

11 

11.00 

0.19 

11.00 

0.24 

11.00 

0.28 

10.99 

0.34 

11 

12 

12.00 

0.21 

12.00 

0.26 

12.00 

0.31 

11.99 

0.37 

12 

13 

13.00 

0.23 

13.00 

0.28 

13.00 

0.34 

12.99 

0.40 

13 

14 

14.00 

0.24 

14.00 

0.31 

14.00 

0.37 

13.99 

0.43 

14 

15 

15.00 

0.26 

15.00 

0.33 

14.99 

0.39 

14.99 

0.46 

15 

16 

16.00 

0.28 

16.00 

0.35 

15.99 

0.42 

15.99 

0.49 

16 

17 

17.00 

0.30 

17.00 

0.37 

16.99 

0.45 

16.99 

0.52 

17 

18 

18.00 

0.31 

18.00 

0.39 

17.99 

0.47 

17.99 

0.55 

18 

19 

19.00 

0.33 

19.00 

0.41 

18.99 

0.50 

18.99 

0.58 

19 

20 

20.00 

0.35 

20.00 

0.44 

19.99 

0.52 

19.99 

0.61 

20 

2-1 

21.00 

0.37 

21.00 

0.46 

20.99 

0.55 

20.99 

0.64 

21 

22 

22.00 

0.38 

21.99 

0.48 

21.99 

0.58 

21.99 

0.67 

22 

23 

23.00 

0.40 

22.99 

0.50 

22.99 

0.60 

22.99 

0.70 

23 

24 

24.00 

0.42 

23.99 

0.52 

23.99 

0.63 

23.99 

0.73 

24 

25 

25.00 

0.44 

24.99 

0.55 

24.99 

0.65 

24.99 

0.76 

25 

26 

26.00 

0.45 

25.99 

0.57 

25.99 

0.68 

25.99 

0.79 

26 

27 

27.00 

0.47 

26.99 

0.59 

26.99 

0.71 

26.99 

0.83 

27 

28 

28.00 

0.49 

27.99 

0.61 

27.99 

0.73 

27.99 

0.86 

28 

29 

29.00 

0.51 

28.99 

0.63 

28.99 

0.76 

28.99 

0.89 

29 

30 

30.00 

.0.52 

29.99 

0.65 

29.99 

0.79 

29.99 

0.92 

30 

31 

31.00 

0.54 

30.99 

0.68 

30.99 

0.81 

30.99 

0.95 

31 

32 

32.00 

'0.56 

31.99 

0.70 

31.99 

0.84 

31.99 

0.98 

32 

33 

32.99 

0.58 

32.99 

0.72 

32.99 

0.86 

32.98 

1.01 

33 

34 

33.99 

0.59 

33.99 

0.74 

33.99 

0.89 

33.98 

1.04 

34 

35 

34.99 

0.61 

34.99 

0.76 

34.99 

0.92 

34.98 

1.07 

35 

36 

35.99 

0.63 

35.99 

0.79 

35.99 

0.94 

35.98 

1.10 

36 

37 

36.99 

0.65 

36.99 

0.81 

36.99 

0.97 

36.98 

1.13 

37 

38 

37.99 

0.66 

37.99 

0.83 

37.99 

0.99 

37.98 

1.16 

38 

39 

38.99 

0.68 

38.99 

0.85 

38.99 

1.02 

38.98 

1.19 

39 

40 

39.99 

0.70 

39.99 

0.87 

39.99 

1.05 

39.98 

1.22 

40 

41 

40.99 

0.72 

40.99 

0.89 

40.99 

1.07 

40.98 

1.25 

41 

42 

41.99 

0.73 

41.99 

0.92 

41.99 

1.10 

41.98 

1.28 

42 

43 

42.99 

0.75 

42.99 

0.94 

42.99 

1.13 

42.98 

1.31 

43 

44 

43.99 

0.77 

43.99 

0.96 

43.99 

1.15 

43.98 

1.34 

44 

45 

44.99 

0.79 

44.99 

0.98 

44.99 

1.18 

44.98 

1.37 

45 

46 

45.99 

0.80 

45.99 

1.00 

45.99 

.1.20 

45.98 

1.40 

46 

47 

46.99 

0.82 

46.99 

1.03 

46.99 

1.23 

46.98 

1.44 

47 

48 

47.99 

0.84 

47.99 

1.05 

47.98 

1.26 

47.98 

1.47 

48 

49 

48.99 

0.86 

48.99 

1.07 

48.98 

1.28 

48.98 

1.50 

49 

50 

49.99 

0.87 

49.99 

1.09 

49.98 

1.31 

49.98 

1.53 

50 

0) 

o 

Jj 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

V 

o 

a 

4-> 

m 

• H 

Q 

89 Deg. 

88$ Deg. 

88$ Deg. 

88$ Deg. 

G 

CTJ 

•4-J 

c n 

• H 

Q 














































































TRAVERSE TABLE 


0 


1 Distance. 

1 Deg. 

i 

1$ Deg. 

U Deg. 

If Deg. 

Distance. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

51 

50.99 

0.89 

50.99 

1.11 

50.98 

1.34 

50.98 

1.56 

51 

52 

51.99 

0.91 

51.99 

1.13 

51.98 

1.36 

51.98 

1.59 

52 

53 

52.99 

0.92 

52.99 

1.16 

52.98 

1.39 

52.98 

1.62 

53 

? 54 

53.99 

0.94 

53.99 

1.18 

53.98 

1.41 

53.97 

1.65 

54 

! 55 

54.99 

0.96 

54.99 

1.20 

54.98 

1.44 

54.97 

1.68 

55 

| 56 

55.99 

0.98 

55.99 

1.22 

55.98 

1.47 

55.97 

1.71 

56 

1 57 

56.99 

0.99 

56.99 

1.24 

56.98 

1.49 

56.97 

1.74 

57 

58 

57.99 

1.01 

57.99 

1.27 

57.98 

1.52 

57.97 

1.77 

58 

59 

58.99 

1.03 

58.99 

1.29 

58.98 

1.54 

58.97 

1.80 

59 

60 

59.99 

1.05 

59.99 

1.31 

59.98 

1.57 

59.97 

1.83 

60 

61 

60.99 

1.06 

60.99 

1.33 

60.98 

1.60 

60.97 

1.86 

61 

62 

61.99 

1.08 

61.99 

1.35 

61.98 

1.62 

61.97 

1.89 

62 

63 

62.99 

1.10 

62.99 

1.37 

62.98 

1.65 

62.97 

1.92 

63 

64 

63.99 

1.12 

63.98 

1.40 

63.98 

1.68 

63.97 

1.95 

64 

65 

64.99 

1.13 

64.98 

1.42 

64.98 

1.70 

64.97 

1.99 

65 

' 66 

65.99 

1.15 

65.98 

1.44 

65.98 

1.73 

65.97 

2.02 

66 

67 

66.99 

1.17 

66.98 

1.46 

66.98 

1.75 

66.97 

2.05 

67 

68 

67.99 

1.19 

67.98 

1.48 

67.98 

1.78 

67.97 

2.08 

68 

69 

68.99 

1.20 

68.98 

1.51 

68.98 

1.81 

68.97 

2.11 

69 

70 

69.99 

1.22 

69.98 

1.53 

69.98 

1.83 

69.97 

2.14 

70 

71 

70.99 

1.24 

70.98 

1.55 

70.98 

1.86 

70.97 

2.17 

71 

i 72 

71.99 

1.26 

71.98 

1.57 

71.98 

1.88 

71.97 

2.20 

72 

73 

72.99 

1.27 

72.98 

1.59 

72.97 

1.91 

72.97 

2.23 

73 

74 

73.99 

1.29 

73.98 

1.61 

73.97 

1.94 

73.97 

2.26 

74 

75 

74.99 

1.31 

74.98 

1.64 

74.97 

1.96 

74.97 

2.29 

75 

' 76 

75.99 

1.33 

75.98 

1.66 

75.97 

1.99 

75.96 

2.32 

76 

77 

76.99 

1.34 

76.98 

1.68 

76.97 

2.02 

76.96 

2.35 

77 

78 

77.99 

1.36 

77.98 

1.70 

77.97 

2.04 

77.96 

2.38 

78 

79 

78.99 

1.38 

78.98 

1.72 

78.97 

2.07 

78.96 

2.41 

79 

80 

79.99 

1.40 

79.98 

1.75 

79.97 

2.09 

79.96 

2.44 

80 

J 81 

80.99 

1.41 

80.98 

1.77 

80.97 

2.12 

80.96 

2.47 

81 

82 

81.99 

1.43 

81.98 

1.79 

81.97 

2.15 

81.96 

2.50 

82 

83 

82.99 

1.45 

82.98 

1.81 

82.97 

2.17 

82.96 

2.53 

83 

84 

83.99 

1.47 

83.98 

1.83 

83.97 

2.20 

83.96 

2.57 

84 

l 85 

84.99 

1.48 

84.98 

1.85 

84.97 

2.23 

84.96 

2.60 

85 

86 

85.99 

1.50 

85.98 

1.88 

85.97 

2.25 

85.96 

2.63 

86 

87 

86.99 

1.52 

86.98 

1.90 

86.97 

2.28 

86.96 

2.66 

87 

88 

87.99 

1.54 

87.98 

1.92 

87.97 

2.30 

87.96 

2.69 

88 

89 

88.99 

1.55 

88.98 

1.94 

88.97 

2.33 

88.96 

2.72 

89 

90 

89.99 

1.57 

89.98 

1.96 

89.97 

2.36 

89.96 

2.75 

90 

91 

90.99 

1.59 

90.98 

1.99 

90.97 

2.38 

90.96 

2.78 

91 

92 

91.99 

1.61 

91.98 

2.01 

91.97 

2.41 

91.96 

2.81 

92 

93 

92.99 

1.62 

92.98 

2.03 

92.97 

2.43 

92.96 

2.84 

93 

94 

93.99 

1.64 

93.98 

2.05 

93.97 

2.46 

93.96 

2.87 

94 

95 

94.99 

1.66 

94.98 

2.07 

94.97 

2.49 

94.96 

2.90 

95 

96 

95.99 

1.68 

95.98 

2.09 

95.97 

2.51 

95.96 

2.94 

96 

97 

96.99 

1.69 

96.98 

2.12 

96.97 

2.54 

96.95 

2.96 

97 

98 

97.99 

1.71 

97.98 

2.14 

97.97 

2.57 

97.95 

2.99 

98 

99 

98.98 

1.73 

98.98 

2.16 

98.97 

2.59 

98.95 

3.02 

99 

100 

99.98 

1.75 | 

99.98 

2.18 

99.97 

2.62 

99.95 

3.05 

100 

Distance. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 1 

Lat. 

Dep. 

Lat. 

Distance. 

89 Deg. 

88f Deg. 

88$ Deg. 1 

i 

88$ Deg. 






































































































6 


TRAVERSE TABLE 


0 

C/3* 

P 

2 Deg. 

Deg. 

| 

2* Deg. 

2| Deg. 

O 

H • 

in 

r-*- 

V 

53 

O 

<t> 

• 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

o 

(6 

1 

1.00 

0.03 

1.00 

0.04 

1.00 

0.04 

1.00 

0.05 

1 

2 

2.00 

0.07 

2.00 

0.08 

2.00 

0.09 

2.00 

0.10 

2 

3 

3.00 

0.10 

3.00 

0.12 

3.00 

0.13 

3.00 

0.14 

3 

4 

4.00 

0.14 

4.00 

0.16 

4.00 

0.17 

4.00 

0.19 

4 

5 

5.00 

0.17 

5.00 

0.20 

5.00 

0.22 

4.99 

0.24 

5 

6 

6.00 

0.21 

6.00 

0.24 

5.99 

0.26 

5.99 

0.29 

6 

7 

7.00 

0.24 

6.99 

0.27 

6.99 

0.31 

6.99 

0.34 

7 

8 

7.99 

0.28 

7.99 

0.31 

7.99 

0.35 

7.99 

0.38 

8 

9 

8.99 

0.31 

8.99 

0.35 

8.99 

0.39 

8.99 

0.43 

9 

10 

9.99 

0.35 

9.99 

0.39 

9.99 

0.44 

9.99 

0.48 

10 

11 

10.99 

0.38 

10.99 

0.43 

10.99 

0.48 

10.99 

0.53 

11 

12 

11.99 

0.42 

11.99 

0.47 

11.99 

0.52 

11.99 

0.58 

12 

13 

12.99 

0.45 

12.99 

0.51 

12.99 

0.57 

12.99 

0.62 

13 

14 

13.99 

0.49 

13.99 

0.55 

13.99 

0.61 

13.98 

0.67 

14 

15 

14.99 

0.52 

14.99 

0.59 

14.99 

0.65 

14.98 

0.72 

15 

16 

15.99 

0.56 

15.99 

0.63 

15.99 

0.70 

15.98 

0.77 

16 

17 

16.99 

0.59 

16.99 

0.67 

16.98 

0.74 

16.98 

0.82 

17 

18 

17.99 

0.63 

17.99 

0.71 

17.98 

0.79 

17.98 

0.86 

18 

19 

18.99 

0.66 

18.99 

0.75 

18.98 

0.83 

18.98 

0.91 

19 

20 

19.99 

0.70 

19.98 

0.79 

19.98 

0.87 

19.98 

0.96 

20 

21 

20.99 

0.73 

20.98 

0.82 

20.98 

0.92 

20.98 

1.01 

21 

22 

21.99 

0.77 

21.98 

0.86 

21.98 

0.96 

21.97 

1.06 

22 

23 

22.99 

0.80 

22.98 

0.90 

22.98 

1.00 

22.97 

1.10 

23 

24 

23.99 

0.84 

23.98 

0.94 

23.98 

1.05 

23.97 

1.15 

24 

25 

24.98 

0.87 

24.98 

0.98 

24.98 

1.09 

24.97 

1.20 

25 

26 

25.98 

0.91 

25.98 

1.02 

25.98 

1.13 

25.97 

1.25 

26 

27 

26.98 

0.94 

26.98 

1.06 

26.97 

1.18 

26.97 

1.30 

27 

28 

27.98 

0.98 

27.98 

1.10 

27.97 

1.22 

27.97 

1.34 

28 

29 

28.98 

1.01 

28.98 

1.14 

28.97 

1.26 

28.97 

1.39 

29 | 

30 

29.98 

1.05 

29.98 

1.18 

29.97 

1.31 

29.97 

1.44 

30 

31 

30.98 

1.03 

30.98 

1.22 

30.97 

1.35 

30.96 

1.49 

31 

32 

31.98 

1.12 

31.98 

1.26 

31.97 

1.40 

31.96 

1.54 

32 

33 

32.98 

1.15 

32.97 

1.30 

32.97 

1.44 

32.96 

1.58 

33 

34 

33.98 

1.19 

33.97 

1.33 

33.97 

1.48 

33.96 

1.63 

34 

35 

34.98 

1.22 

34.97 

1.37 

34.97 

1.53 

34.96 

1.68 

35 

36 

35.98 

1.26 

35.97 

1.41 

35.97 

1.57 

35.96 

1.73 

36 

37 

36.98 

1.29 

36.97 

1.45 

36.96 

1.61 

36.96 

1.78 

37 

38 

37.98 

1.33 

37.97 

1.49 

37.96 

1.66 

37.96 

1.82 

38 

39 

38.98 

1.36 

38.97 

1.53 

38.96 

1.70 

38.96 

1.87 

39 | 

40 

39.98 

1.40 

39.97 

1.57 

39.96 

1.75 

39.95 

1.92 

: 40 

41 

40.98 

1.43 

40.97 

1.61 

40.96 

1.77 

40.95 

1.97 

i 41 

42 

41.97 

1.47 

41.97 

1.65 

41.96 

1.83 

41.95 

2.02 

42 

43 

42.97 

1.50 

42.97 

1.69 

42.96 

1.88 

42.95 

2.06 

43 

44 

43.97 

1.54 

43.97 

1.73 

43.96 

1.92 

43.95 

2.11 

44 

45 

44.97 

1.57 

44.97 

1.77 

44.96 

1.96 

44.95 

2.16 

45 

46 

45.97 

1.61 

| 45.96 

1.81 

45.96 

2.01 

45.95 

2.21 

46 

47 

46.97 

1.64 

| 46.96 

1.85 

46.96 

2.05 

46.95 

2.25 

47 

: 48 

47.97 

1.68 

! 47.96 

1.88 

47.95 

2.09 

47.95 

2.30 

48 

1 49 

48.97 

1.71 

! 48.96 

1.92 

48.95 

2.14 

48.94 

2.35 

49 

! 50 

49.97 

1.74 

1 49.96 

1.96 

49.95 

2.18 

49.94 

2.40 

50 

• 

<11 

o 

c 

Dep. 

Lat. 

* Dep. 

.1 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

6 

o 

cc 

4-> 

(f) 

• H 

Q 

88 Deg. 

87$ Deg. 

} 

87 i Deg. 

87$ 

! 

Deg. 

£« 

ct 

Kfi 

S 


























































































































TRAVERSE TABLE 


7 


S 5 

fl r/i * 

1 5? 

2 Deg. 

2* Deg. 

2J Deg. 

2| Deg. 

0 

. 

C/> ; 

r- 1- , 

» i 

1 <5 

1 ' ? 

Lat. 

Dep. 

Lat. 

Dep. i 

Lat. 

Dep. 

Lat. 

Dep. 

W ; 

O i 
a 

’ j 

51 

50.97 

1.78 

50.96 

2.00 

50.95 

2.22 

50.94 

2.45 

51 

52 

51.97 

1.81 

51.96 

2.04 | 

51.95 

2.27 

51.94 

2.50 

52 

53 

52.97 

1.85 

52.96 

2.08 

52.95 

2.31 

52.94 

2.54 

53 

54 

53.97 

1.88 

53.96 

2.12 | 

53.95 

2.36 

53.94 

2.59 

54 

55 

54.97 

1.92 

54.96 

2.16 

54.95 

2.40 

54.94 

2.64 

55 

56 

55.97 

1.95 

55.96 

2.20 

55.95 

2.44 

55.94 

2.69 

56 

57 

56.97 

1.99 

56.96 

2.24 

56.95 

2.49 

56.93 

2.73 

57 

58 

57.96 

2.02 

57.96 

2.28 

57.94 

2.53 

57.93 

2.78 

58 

59 

58.96 

2.06 

58.95 

2.32 

58.94 

2.57 

58.93 

2.83 

59 

J 60 

1 

59.96 

2.09 

59.95 

2.36 

59.94 

2.62 

59.93 

2.88 

60 

61 

60.96 

2.13 

60.95 

2.39 

60.94 

2.66 

60.93 

2.93 

61 

62 

61.96 

2.16 

61.95 

2.43 

61.94 

2.70 

61.93 

2.97 

62 

63 

62.96 

2.20 

62.95 

2.47 

62.94 

2.75 

62.93 

3.02 

63 

64 

63.96 

2.23 

63.95 

2.51 

63.94 

2.79 

63.93 

3.07 

64 

65 

64.96 

2.27 

64.95 

2.55 

64.94 

2.84 

64.93 

3.12 

65 

66 

65.96 

2.30 

65.95 

2.59 

65.94 

2.88 

65.92 

3.17 

66 

67 

66.96 

2.34 

66.95 

2.63 

66.94 

2.92 

66.92 

3.21 

67 

68 

67.96 

2.37 

67.95 

2.67 

67.94 

2.97 

67.92 

3.26 

68 

69 

68.96 

2.41 

68.95 

2.71 

68.93 

3.01 

68.92 

3.31 

69 

70 

69.96 

2.44 

69.95 

2.75 

69.93 

3.05 

69.92 

3.36 

70 

71 

70.96 

2.48 

70.95 

2.79 

70.93 

3.10 

70.92 

3.41 

71 

72 

71.96 

2.51 

71.94 

2.83 

71.93 

3.14 

71.92 

3.45 

72 

73 

72.96 

2.55 

72.94 

2.87 

72.93 

3.18 

72.92 

3.50 

73 

74 

73.95 

2.58 

73.94 

2.91 

73.93 

3.23 

73.91 

3.55 

74 

75 

74.95 

2.62 

74.94 

2.94 

74.93 

3.27 

74.91 

3.60 

75 

76 

75.95 

2.65 

75.94 

2.98 

75.93 

3.31 

75.91 

3.65 

76 

77 

76.95 

2.69 

76.94 

3.02 

76.93 

3.36 

76.91 

3.70 

77 

78 

77.95 

2.72 

77.94 

3.06 

77.93 

3.40 

77.91 

3.74 

78 

79 

78.95 

2.76 

78.94 

3.10 

78.92 

3.45 

78.91 

3.79 

79 

80 

79.95 

- 2.79 

79.94 

3.14 

79.92 

3.49 

79.91 

3.84 

80 

I 81 

80.95 

2.83 

80.94 

3.18 

80.92 

3.53 

80.91 

3.89 

81 

82 

81.95 

2.86 

81.94 

3.22 

81.92 

3.58 

81.91 

3.93 

82 

1 83 

82.95 

2.90 

82.94 

3.26 

82.92 

3.62 

82.90 

3.98 

83 

| 84 

83.95 

2.93 

83.94 

3.30 

83.92 

3.66 

83.90 

4.03 

84 

8 85 

84.95 

2.97 

84.93 

3.34 

84.92 

3.71 

84.90 

4.08 

85 

I 86 

85.95 

3.00 

85.93 

3.38 

85.92 

3.75 

85.90 

4.13 

86 

I 87 

86.95 

3.04 

86.93 

3.42 

86.92 

3.79 

86.90 

4.17 

87 

1 88 

87.95 

3.07 

87.93 

3.45 

87.92 

3.84 

87.90 

4.22 

88 

i 89 

88.95 

3.11 

88.93 

3.49 

88.92 

3.88 

88.90 

4.27 

89 

I 80 

89.95 

3.14 

89.93 

3.53 

89.91 

3.93 

89.90 

4.32 

90 

| 91 

90.95 

3.18 

90.93 

3.57 

90.91 

3.97 

90.90 

4; 37 

91 

I 92 

91.94 

3.21 

91.93 

3.61 

91.91 

4.01 

91.89 

4.41 

92 

j 93 

92.94 

3.25 

92.93 

3.65 

92.91 

4.06 

92.89 

4.46 

93 

| 94 

93.94 

3.28 

93.93 

3.69 

93.91 

4.10 

93.89 

4.51 

94 

95 

94.94 

3.32 

94.93 

3.73 

94.91 

4.14 

94.89 

4.56 

95 

96 

95.94 

3.35 

95.93 

3.77 

95.91 

4.19 

95.89 

4.61 

96 

97 

96.94 

3.39 

96.93 

3.81 

96.91 

4.23 

96.89 

4.65 

97 

98 

97.94 

3.42 

97.92 

3.85 

97.91 

4.27 

97.89 

4.70 

98 

99 

98.94 

3.46 

98.92 

3.89 

98.91 

4.32 

98.89 

4.75 

99 

100 

99.94 

3.49 

99.92 

3.93 

99.91 

4.36 

99.88 

4.80 

100 

6 

o 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. i 

Lat. 

<u" 

o 

£ 

3 

trt 

Q 

- 

88 Deg. 

CO 

Deg. 

87£ Deg. 

i 

87* Deg. 

a 

*-) 

05 

• H 

Q 


































































































8 


TRAVERSE TABLE 


1 Distance. 

3 Deg. 

3} Deg. 

3£ Deg. 

3| Deg. 

Distance. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

1 

1.00 

0.05 

1.00 

0.06 

1.00 

0.06 

1.00 

0.06 

1 

2 

2.00 

0.10 

2.00 

0.11 

2.00 

0.12 

2.00 

0.13 

2 

3 

3.00 

0.16 

3.00 

0.17 

2.99 

0.18 

2.99 

0.20 

3 

4 

3.99 

0.21 

3.99 

0.23 

3.99 

0.24 

3.99 

0.26 

4 

5 

4.99 

0.26 

4.99 

0.28 

4.99 

0.31 

4.99 

0.33 

5 

6 

5.99 

0.31 

5.99 

0.34 

5.99 

0.37 

5.99 

0.39 

6 

7 

6.99 

0.37 

6.99 

0.40 

6.99 

0.43 

6.99 

0.46 

7 

8 

7.99 

0.42 

7.99 

0.45 

7.99 

0.49 

7.98 

0.52 

8 

9 

8.99 

0.47 

8.99 

0.51 

8.98 

0.55 

8.98 

0.59 

9 

10 

9.99 

0.52 

9.98 

0.57 

9.98 

0.61 

9.98 

0.65 

10 

11 

10.98 

0.58 

10.98 

0.62 

10.98 

0.67 

10.98 

0.72 

11 

12 

11.98 

0.63 

11.98 

0.68 

11.98 

0.73 

11.97 

0.78 

12 

13 

12.98 

0.68 

12.98 

0.73 

12.98 

0.79 

12.97 

0.85 

13 

14 

13.98 

0.73 

13.98 

0.79 

13.97 

0.85 

13.97 

0.92 

14 

15 

14.98 

0.79 

14.98 

0.85 

14.97 

0.92 

14.97 

0.98 

15 

16 

15.98 

0.84 

15.97 

0.91 

15.97 

0.98 

15.97 

1.05 

16 

17 

16.98 

0.89 

16.97 

0.96 

16.97 

1.04 

16.96 

1.11 

17 

18 

17.98 

0.94 

17.97 

1.02 

17.97 

1.10 

17.96 

1.18 

18 

19 

18.98 

0.99 

18.97 

1.08 

18.96 

1.16 

18.96 

1.24 

19 

20 

19.97 

1.05 

19.97 

1.13 

19.96 

1.22 

19.96 

1.31 

20 

21 

20.97 

1.10 

20.97 

1.19 

20.96 

1.28 

20.96 

1.37 

21 

22 

21.97 

1.15 

21.96 

1.25 

21.96 

1.34 

21.95 

1.44 

22 

23 

22.97 

1.20 

22.96 

1.30 

22.96 

1.40 

22.95 

1.50 

23 

24 

23.97 

1.26 

23.96 

1.36 

23.96 

1.47 

23.95 

1.57 

24 

25 

24.97 

1.31 

24.96 

1.42 

24.95 

1.53 

24.95 

1.64 

25 

26 

25.96 

1.36 

25.96 

1.47 

25.95 

1.59 

25.94 

1.70 

26 

27 

26.96 

1.41 

26.96 

1.53 

26.95 

1.65 

26.94 

1.77 

27 

28 

27.96 

1.47 

27.95 

1.59 

27.95 

1.71 

27.94 

1.83 

28 

29 

28.96 

1.52 

28.95 

1.64 

28.95 

1.77 

28.94 

1.90 

29 

30 

29.96 

1.57 

29.95 

1.70 

29.94 

1.83 

1 

29.94 

1.96 

30 

31 

30.96 

1.62 

30.95 

1.76 

30.94 

1.89 

30.93 

2.03 

31 

32 

31.96 

1.67 

31.95 

1.81 

31.94 

1.95 

31.93 

2.09 

32 

33 

32.95 

1.73 

32.95 

1.87 

32.94 

2.01 

32.93 

2.16 

33 

34 

33.95 

1.78 

33.95 

1.93 

33.94 

2.08 

33.93 

2.22 

34 

35 

34.95 

1.83 

34.94 

1.98 

34.93 

2.14 

34.92 

2.29 

35 

36 

35.95 

1.88 

35.94 

2.04 

35.93 

2.20 

35.92 

2.35 

36 

37 

36.95 

1.94 

36.94 

2.10 

36.93 

2.26 

36.92 

2.42 

37 

38 

37.95 

1.99 

37.94 

2.15 

37.93 

2.32 

37.92 

2.49 

38 

39 

38.95 

2.04 

38.94 

2.21 

38.93 

2.38 

38.92 

2.55 

39 

40 

39.95 

2.09 

39.94 

2.27 

39.93 

2.44 

39.91 

2.62 

40 

41 

40.94 

2.15 

40.93 

2.32 

40.92 

2.50 

40.91 

2.68 

41 

42 

41.94 

2.20 

41.93 

2.38 

41.92 

2.56 

41.91 

2.75 

42 

43 

42.94 

2.25 

42.93 

2.44 

42.92 

.2.63 

42.91 

2.81 

43 

44 

43.94 

2.30 

43.93 

2.49 

43.92 

2.69 

43.91 

2.88 

44 

45 

44.94 

2.36 

44.93 

2.55 

44.92 

2.75 

44.90 

2.94 

45 

46 

45.94 

2.41 

45.93 

2.61 

45.91 

2.81 

45.90 

3.01 

46 

47 

46.94 

2.46 

46.92 

2.66 

46.91 

2.87 

46.90 

3.07 

47 

48 

47.93 

2.51 

47.92 

2.72 

47.91 

2.93- 

47.90 

3.14 

48 

49 

48.93 

2.56 

48.92 

2.78 

48.91 

2.99 

48.90 

3.20 

49 

50 

49.93 

2.62 

49.92 

2.83 

49.91 

3.05 

49.89 

3.27 

50 

Distance. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

6 

o 

£ 

cn 

• H 

G 

87 Deg. 

86| Deg. | 

86^ Deg. 

86i Deg. 

























































































TRAVERSE TABLE 


9 


p-- 

o 
>— • 

C/3 

<-»* 

P 

3 

3 Deg. 

Deg. 

3i Deg. 

3| Deg. | 

e 

h-> • 

ID 

P 

o 

• 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

3 

o 

fD 

51 

50.93 

2.67 

50.92 

2.89 

50.90 

3.11 

50.89 

3.34 

51 

52 

51.93 

2.72 

51.92 

2.95 

51.90 

3.17 

51.89 

3.40 

52 

53 

52.93 

2.77 

52.91 

3.00 

52.90 

3.24 

52.89 

3.47 

53 

54 

53.93 

2.83 

53.91 

3.06 

53.90 

3.30 

53.88 

3.53 

54 

55 

54.92 

2.88 

54.91 

3.12 

54.90 

3.36 

54.88 

3.60 

55 

56 

55.92 

2.93 

55.91 

3.17 

55.90 

3.42 

55.88 

3.66 

56 

57 

56.92 

2.98 

56.91 

3.23 

56.89 

3.48 

56.88 

3.73 

57 

58 

57.92 

3.04 

57.91 

3.29 

57.89 

3.54 

57.88 

3.79 

58 

59 

58.92 

3.09 

58.91 

3.34 

58.89 

3.60 

58.87 

3.86 

59 

60 

59.92 

3.14 

59.90 

3.40 

59.89 

3.66 

59.87 

3.92 

60 

61 

60.92 

3.19 

60.90 

3.46 

60.89 

3.72 

60.87 

3.99 

61 

62 

61.92 

3.24 

61.90 

3.51 

61.88 

3.79 

61.87 

4.05 

62 

63 

62.91 

3.30 

62.90 

3.57 

62.88 

3.85 

62.87 

4.12 

63 

64 

63.91 

3.35 

63.90 

3.63 

63.88 

3.91 

63.86 

4.19 

64 

65 

64.91 

3.40 

64.90 

3.69 

64.88 

3.97 

64.86 

4.25 

65 

66 

65.91 

3.45 

65.89 

3.74 

65.88 

4.03 

65.86 

4.32 

66 

67 

66.91 

3.51 

66.89 

3.80 

66.88 

4.09 

66.86 

4.38 

67 

68 

67.91 

3.56 

67.89 

3.86 

67.87 

4.15 

67.85 

4.45 

68 

69 

68.91 

3.61 

68.89 

3.91 

68.87 

4.21 

68.85 

4.51 

69 

70 

69.90 

3.66 

69.89 

3.97 

69.87 

4.27 

69.85 

4.58 

70 

71 

70.90 

3.72 

70.89 

4.03 

70.87 

4.33 

70.85 

4.64 

71 

72 

71.90 

3.77 

71.88 

4.08 

71.87 

4.40 

71.85 

4.71 

72 

73 

72.90 

3.82 

72.88 

4.14 

72.86 

4.46 

72.84 

4.77 

73 

74 

73.90 

3.87 

73.88 

4.20 

73.86 

4.52 

73.84 

4.84 

74 

75 

74.90 

3.93 

74.88 

4.25 

74.86 

4.58 

74.84 

4.91 

75 

76 

75.90 

3.98 

75.88 

4.31 

75.86 

4.64 

75.84 

4.97 

76 

77 

76.89 

4.03 

76.88 

4.37 

76.86 

4.70 

76.84 

5.04 

77 

78 

77.89 

4.08 

77.87 

4.42 

77.85 

4.76 

77.83 

5.10 

78 

79 

78.89 

4.13 

78.87 

4.48 

78.85 

4.82 

78.83 

5.17 

79 

80 

79.89 

4.19 

79.87 

4.54 

79.85 

4.88 

79.83 

5.23 

80 

81 

80.89 

4.24 

80.87 

4.59 

80.85 

4.94 

80.83 

5.30 

81 

82 

81.89 

4.29 

81.87 

4.65 

81.85 

5.01 

81.82 

5.36 

82 

83 

82.89 

4.34 

82.87 

4.71 

82.85 

5.07 

82.82 

5.43 

83 

84 

83.88 

4.40 

83.86 

4.76 

83.84 

5.13 

83.82 

5.49 

84 

85 

84.88 

4.45 

84.86 

4.82 

84.84 

5.19 

84.82 

5.56 

85 

86 

85.88 

4.50 

85.86 

4.88 

85.84 

5.25 

85.82 

5.62 

86 

87 

86.88 

4.55 

86.86 

4.93 

86.84 

5.31 ' 

86.81 

5.69 

87 

88 

87.88 

4.61 

87.86 

4.99 

87.84 

5.37 

87.81 

5.76 

88 

89 

88.88 

4.66 

88.86 

5.05 

88.83 

5.43 

88.81 

5.82 

89 

90 

89.88 

4.71 

89.86 

5.10 

89.83 

5.49 

89.81 

5.89 

90 

91 

90.88 

4.76 

90.85 

5.16 

90.83 

5.56 

90.81 

5.95 

91 

92 

91.87 

4.81 

91.85 

5.22 

91.83 

5.62 

91.80 

6 .'02 

92 

93 

92.87 

4.87 

92.85 

5.27 

92.83 

5.68 

92.80 

6.08 

93 

94 

93.87 

4.92 

93.85 

5.33 

93.82 

5.74 

93.80 

6.15 

94 

95 

94.87 

4.97 

94.85 

5.39 

94.82 

5.80 

94.80 

6.21 

95 

96 

95.87 

5.02 

95.85 

5.44 

95.82 

5.86 

95.79 

6.28 

96 

97 

96.87 

5.08 

96.84 

5.50 

96.82 

5.92 

96.79 

6.34 

97 

98 

97.87 

5.13 

97.84 

5.56 

97.82 

5.98 

97.79 

6.41 

98 

99 

98.86 

5.18 

98.84 

5.61 

98.82 

6.04 

98.79 

6.47 

99 

100 

99.86 

5.23 

99.84 

5.67 

99.81 

6.10 

99.79 

6.54 

100 

5 

o 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

6 

G 

in 

3 

87 Deg. 

86| Deg. 

86i Deg. 

86| Deg. 

c6 

CO 

• H 

Q 


B 




























































































10 TRAVERSE TABLE. 


a 

h— • 

C/7 

r-t- 

p 

4 Deg. 

4* 

Deg. 

4 h Deg. 

4| 

Deg. 

C |j 

go' I 

1 

o 

o 

? 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

S I 

1 

1.00 

0.07 

1.00 

0.07 

1.00 

0.08 

1.00 

0.08 

1 I 

2 

2.00 

0.14 

1.99 

0.15 

1.99 

0.16 

1.99 

0.17 

2 

3 

2.99 

0.21 

2.99 

0.22 

2.99 

0.24 

2.99 

0.25 

3 | 

4 

3.99 

0.28 

3.99 

0.30 

3.99 

0.31 

3.98 

0.33 

4 || 

5 

4.99 

0.35 

4.99 

0.37 

4.98 

0.39 

4.98 

0.41 

5 

6 

5.99 

0.42 

5.98 

0.44 

5.98 

0.47 

5.98 

0.50 

6 | 

7 

6.98 

0.49 

6.98 

0.52 

6.98 

0.55 

6.97 

0.58 

7 j 

8 

7.98 

0.56 

7.98 

0.59 

7.98 

0.63 

7.97 

0.66 

8 1 

9 

8.98 

0.63 

8.98 

0.67 

8.97 

0.71 

8.97 

0.75 

9 J 

10 

9.98 

0.70 

9.97 

0.74 

9.97 

0.78 

9.97 

0.83 

10 1 

11 

10.97 

0.77 

10.97 

0.82 

10.97 

0.86 

10.96 

0.91 

n j 

12 

11.97 

0.84 

11.97 

0.89 

11.96 

0.94 

11.96 

0.99 

12 j 

13 

12.97 

0.91 

12.96 

0.96 

12.96 

1.02 

12.96 

1.08 

13 

14 

13.97 

0.98 

13.96 

1.04 

13.96 

1.10 

13.95 

1.16 

14 

15 

14.96 

1.05 

14.96 

1.11 

14.95 

1.18 

14.95 

1.24 

15 J 

16 

15.96 

1.12 

15.96 

1.19 

15.95 

1.26 

15.95 

1.32 

16 

17 

16.96 

1.19 

16.95 

1.26 

16.95 

1.33 

16.94 

1.41 

17 

18 

17.96 

1.26 

17.95 

1.33 

17.94 

1.41 

17.94 

1.49 

18 

19 

18.95 

1.33 

18.95 

1.40 

18.94 

1.49 

18.93 

1.57 

19 J 

20 

19.95 

1.40 

19.95 

1.48 

19.94 

1.57 

19.93 

1.66 

20 I 

21 

20.95 

1.46 

20.94 

1.56 

20.94 

1.65 

20.93 

1.74 

21 h 

22 

21.95. 

1.53 

21.94 

1.63 

21.93 

1.73 

21.92 

1.82 

22 | 

23 

22.94 

1.60 

22.94 

1.70 

22.93 

1.80 

22.92 

1.90 

23 |j 

24 

23.94 

1.67 

23.93 

1.78 

23.93 

1.88 

23.92 

1.99 

24 [ 

25 

24.94 

1.74 

24.93 

1.85 

24.92 

1.96 

24.91 

2.07 

25 if 

26 

25.94 

1.81 

25-93 

1.93 

25.92 

2.04 

25.91 

2.15 

26 ij 

27. 

26.93 

1.88 

26.93 

2.00 

26.92 

2.12 

26.91 

2.24 

27 j 

28 

27.93 

1.95 

27.92 

2.08 

27.91 

2.20 

27.90 

2.32 

28 

29 

28.93 

2.02 

28.92 

2.15- 

28.91 

2.28 

28.90 

2.40 

29 ! 

30 

29.93 

2.09 

29.92 

2.22 

29.91 - 

2.35 

29.90 

2.48 

30 j 

31 

30.92 

2.16 

30.91 

2.30 

30.90 

2.43 

30.89 

2.57 

31 | 

32 

31.92 

2.23 

31.91 

2.37 

31.90 

2.51 

31.89 

2.65 

32 [ 

33 

32.92 

2.30 

32.91 

2.45 

32.90 

2.59 

32.89 

2.73 

33 If 

34 

33.92 

2.37 

33.91 

2.52 

33.90 

2.67. 

33.88 

2.82 

34 | 

1 35 

34.91 

2.44 

34.90 

2.59 

34.89 

2.75 

34.88 

2.90 

35 1 

36 

35.91 

2.51 

35.90 

2.67 

35.89 

2.82 

35.88 

2.98 

36 ij 

37 

36.91 

2.58 

36.90 

2.74 

36.89 

2.90 

36.87 

3.06 

37 1 

38 

37.91 

2.65 

37.90 

2.82 

37.88 

2.98 

37.87 

3.15 

38 | 

39 

38.90 

2.72 

38.89 

2.89 

38.88 

3.06 

38.87 

3.23 

39 j 

40 

39.90 

2.79 

39.89 

2.96 

39.88 

3.14 

39.86 

3.31 

40 if 

41 

40.90 

2.86 

40.89 

3.04 

40.87 

3.22 

40.86 

3.40 

41 ! 

42 

41.90 

2.93 

41.88 

3.11 

41.87 

3.30 

41.86 

3.48 

42 j 

43 

42.90 

3.00 

42.88 

3.19 

42.87 

3.37 

42.85 

3.56 

43 j 

44 

43.89 

3.07 

43.88 

3.26 

43.86 

3.45 

43.85 

3.64 

44 j 

45 

44.89 

3.14 

44.88 

3\ 33 

44.86 

3.53 

44.85 

3.73 

45 j 

46 

45.89 

3.21 

45.87 

3.41 

45.86 

3.61 

45.84 

3.81 

46 I 

47 

46.89 

3.28 

46.87 

3.48 

46.86 

3.69 

46.84 

3.89 

47 j 

48 

47.88 

3.35 

47.87 

3.56 

47.85 

3.77 

47.84 

3.97 

48 j 

49 

48.88 

3.42 

48.87 

3.63 

48.85 

3.84 

48.83 

4.06 

49 >| 

50 

49.88 

3.49 

49.86 

3.71 

49.85 

3.92 

49.83 

4.14 

50l 

• 

o 

u 

a 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. | 

Lat. 

Dep. 

Lat. 

<J j 

o 

1 d 
+■) 

CO 
• *-< 

Q 

t 

86 Deg. 

85| Deg. 

8 oh Deg. 

85£ Deg. 

0 j 

a 

+-> i 

CO 

• H 

Q 

















































































































TRAVERSE TABLE 


11 


o 

K-. 

« n 

r+- 

P 

a 

4 Deg. 

4* 

Deg. 

4i Deg. 

4| 

Deg. 

d 

v-». 

CO 

ft* 

P 

o 

i <T> 

• 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

3 

o 

CD 

• 

! 51 

50.88 

3.56 

50.86 

3.78 

50.84 

4.00 

50.82 

4.22 

51 

52 

51.87 

3.63 

51.86 

3.85 

51.84 

4.08 

51.82 

4.31 

52 

53 

52.87 

3.70 

52.85 

3.93 

52.84 

4.16 

52.82 

4.39 

53 

| 54 

53.87 

3.77 

53.85 

4.00 

53.83 

4.24 

53.81 

4.47 

54 

55 

54.87 

3.84 

54.85 

4.08 

54.83 

4.32 

54.81 

4.55 

55 

56 

55.86 

3.91 

55.85 

4.15 

55.83 

4.39 

55.81 

4.64 

56 

57 

56.86 

3.98 

56.84 

4.22 

56.82 

4.47 

56.80 

4.72 

57 

' 58 

57.86 

4.05 

57.84 

4.30 

57.82 

4.55 

57.80 

4.80 

58 

59 

58.86 

4.12 

58.84 

4.37 

58.82 

4.63 

58.80 

4.89 

59 

60 

59.85 

4.19 

59.84 

4.45 

59.82 

4.71 

59.79 

4.97 

60 

61 

60.85 

4.26 

60.83 

4.52 

60.81 

4.79 

60.79 

5.05 

61 

62 

61.85 

4.32 

61.83 

4.59 

61.81 

4.86 

61.79 

5.13 

62 

63 

62.85 

4.39 

62.83 

4.67 

62.81 

4.94 

62.78 

5.22 

63 

64 

63.84 

4.46 

63.82 

4.74 

63.80 

5.02 

63.78 

5.30 

64 

65 

64.84 

4.53 

64.82 

4.82 

64.80 

5.10 

64.78 

5.38 

65 

66 

65.84 

4.60 

65.82 

4.89 

65.80 

5.18 

65.77 

5.47 

66 

67 

66.84 

4.67 

66.82 

4.97 

66.79 

5.26 

66.77 

5.55 

67 

68 

67.83 

4.74 

67.81 

5.04 

67.79 

5.34 

67.77 

5.63 

68 

69 

68.83 

4.81 

68.81 

5.11 

68.79 

5.41 

68.76 

5.71 

69 

70 

69.83 

4.88 

69.81 

5.19 

69.78 

5.49 

69.76 

5.80 

70 

71 

70.83 

4.95 

70.80 

5.26 

70.78 

5.57 

70.76 

5.88 

71 

72 

71.82 

5.02 

71.80 

5.34 

71.78 

5.65 

71.75 

5.96 

72 

73 

72.82 

5.09 

72.80 

5.41 

72.77 

5.73 

72.75 

6.04 

73 

74 

73.82 

5.16 

73.80 

5.48 

73.77 

5.81 

73.75 

6.13 

74 

75 

74.82 

5.23 

74.79 

5.56 

74.77 

5.88 

74.74 

6.21 

75 

76 

75.81 

5.30 

75.79 

5.63 

75.77 

5.96 

75.74 

6.29 

76 

77 

76.81 

5.37 

76.79 

5.71 

76.76 

6.04 

76.74 

6.38 

77 

78 

77.81 

5.44 

77.79 

5.78 

77.76 

6.12 

77.73 

6.46 

78 

79 

78.81 

5.51 

78.78 

5.85 

78.76 

6.20 

78.73 

6.54 

79 

80 

79.81 

5.58 

79.78 

5.93 

79.75 

6.28 

79.73 

6.62 

80 

81 

80.80 

5.65 

80.78 

6.00 

80.75 

6.36 

80.72 

6.71 

81 

82 

81.80 

5.72 

81.78 

6.08 

81.75 

6.43 

81.72 

6.79 

82 

83 

82.80 

5.79 

82.77 

6.15 

82.74 

6.51 

82.71 

6.87 

83 

84 

83.80 

5.86 

83.77 

6.23 

83.74 

6.59 

83.71 

6.96 

84 

85 

84.79 

5.93 

84.77 

6.30 

84.74 

6.67 

84.71 

7.04 

85 

86 

85.79 

6.00 

85.76 

6.37 

85.73 

6.75 

85.70 

7.12 

86 

87 

86.79 

6.07 

86.76 

6.45 

86.73 

6.83 

86.70 

7.20 

87 

88 

87.79 

6.14 

87.76 

6.52 

87.73 

6.90 

87.70 

7.29 

88 

89 

88.78 

6.21 

88.76 

6.60 

88.73 

6.98 

88.70 

7.37 

89 

90 | 

89.78 

6.28 

89.75 

6.67 ; 

89,72 

7.06 

89.69 

7.45 

90 

91 

90.78 

6.35 

90.75 

6.74 

90.72 

7.14 

90.69 

7.54 

91 

92 

91.78 

6.42 

91.75 

6.82 

91.72 

7.22 

91.68 

7.62 

92 

93 

92.77 

6.49 

92.74 

6.89 [ 

92.71 

7.30 

92.68 

7.70 

93 

94 

93.77 

6.56 

93.74 

6.97 | 

93.71 

7.38 

93.68 

7.78 

94 

95 

94.77 

6.63 

94.74 

7.04 

94.71 

7.45 

94.67 

7.87 

95 

96 

95.77 

6.70 

95.74 

7.11 

95.70 

7.53 

95.67 

7.95 

96 

97 i 

96.76 

6.77 

96.73 

7.19 

96.70 

7.61 

96.67 

8.03 

97 

98 ! 

97.76 

6.84 

97.73 

7.26 

97.70 

7.69 

97.66 

8.12 

98 

99 

98.76 

6.91 

98.73 

7.34 

98.69 

7.77 

98.66 

8.20 

99 

100 I 

i 

99.76 

6.98 

99.73 

7.41 

99.69 

7.85 

99.66 

8.28 

100 

— 

<u 

o 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

• 

<D 

O 

a 

.7 

in 

• 

Q 

1 —— 

86 Deg. 

85f Deg. 

85 £ Deg. 

85$ Deg. 

• d 

■4-> 

m 

a 




















































































































12 


TRAVERSE TABLE 


I Distance. 

5 Deg. 

r 

5} Deg. 

5^ Deg. 

5£ Deg. 

1 Distance. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

1 

1.00 

0.09 

1.00 

0.09 

1.00 

0.10 

0.99 

0.10 

1 

2 

1.99 

0.17 

1.99 

0.18 

1.99 

0.19 

1.99 

0.20 

2 

3 

2.99 

0.26 

2.99 

0.27 

2.99 

0.29 

2.98 

0.30 

3 | 

4 

3.98 

0.35 

3.98 

0.37 

3.98 

0.38 

3.98 

0.40 

4 

5 

4.98 

0.44 

4.98 

0.46 

4.98 

0.48 

4.97 

0.50 

5 

6 

5.98 

0.52 

5.97 

0.55 

5.97 

0.58 

5.97 

0.60 

6 

7 

6.97 

0.61 

6.97 

0.64 

6.97 

0.67 

6.96 

0.70 

7 

8 

7.97 

0.70 

7.97 

0.73 

7.96 

0.76 

7.96 

0.80 

8 

9 

8.97 

0.78 

8.96 

0.82 

8.96 

0.86 

8.95 

0.90 

9 

10 

9.96 

0.87 

9.96 

0.92 

9.95 

0.96 | 

9.95 

1.00 

10 

11 

10.96 

0.96 

10.95 

1.01 

10.95 

1.05 

10.94 

1.10 

11 

12 

11.95 

1.05 

11.95 

1.10 

11.94 

1.15 

11.94 

1.20 

12 

13 

12.95 

1.13 

12.95 

1.19 

12.94 

1.25 

12.93 

1.30 

13 

14 

13.95 

1.22 

13.94 

1.28 

13.94 

1.34 

13.93 

1.40 

14 

15 

14.94 

1.31 

14.94 

1.37 

14.93 

1.44 

14.92 

1.50 

15 

16 

15.94 

1.39 

15.93 

1.46 

15.93 

1.53 

15.92 

1.60 

16 

17 

16.94 

1.48 

16.93 

1.56 

16.92 

1.63 

16.91 

1.70 

17 

18 

17.93 

1.57 

17.92 

1.65 

17.92 

1.73 

17.91 

1.80 

18 

19 

18.93 

1.66 

18.92 

1.74 

18.91 

1.82 

18.90 

1.90 

19 

20 

19.92 

1.74 

19.92 

1.83 

19.91 

1.92 

19.90 

2.00 

20 

21 

20.92 

1.83 

20.91 

1.92 

20.90 

2.01 

20.89 

2.10 

21 

22 

21.92 

1.92 

21.91 

2.01 

21.90 

2.11 

21.89 

2.20 

22 

23 

22.91 

2.00 

22.90 

2.10 

22.89 

2.20 

22.88 

2.30 

23 

24 

23.91 

2.09 

23.90 

2.20 

23.89 

2.30 

23.88 

2.40 

24 ; 

25 

24.90 

2.18 

24.90 

2.29 

24.88 

2.40 

24.87 

2.50 

25 

26 

25.90 

2.27 

25.89 

2.38 

25.88 

2.49 

25.87 

2.60 

26 

27 

26.90 

2.35 

26.89 

2.47 

26.88 

2.59 

26.86 

2.71 

27 

28 

27.89 

2.44 

27.88 

2.56 

27.87 

2.68 

27.86 

2.81 

28 

| 29 

28.89 

2.53 

28.88 

2.65 

28.87 

2.78 

28.85 

2.91 

29 

30 

29.89 

2.61 

29.87 

2.75 

29.86 

2.88 

29.85 

3.01 

30 

I 31 

30.88 

2.70 

30.87 

2.84 

30.86 

2.97 

30.84 

3.11 

31 

32 

31.88 

2.79 

31.87 

2.93 

31.85 

3.07 

31.84 

3.21 

32 

33 

32.87 

2.88 

32.86 

3.02 

32.85 

3.16 

32.83 

3.31 

33 

34 

33.87 

2.96 

33.86 

3.11 

33.84 

3.26 

33.83 

3.41 

34 

35 

34.87 

3.05 

34.85 

3.20 

34.84 

3.35 

34.82 

3.51 

35 

36 

35.86 

3.14 

35.85 

3.29 

35.83 

3.45 

35.82 

3.61 

36 

37 

36.86 

3.22 

36.84 

3.39 

36.83 

3.55 

36.81 

3.71 

37 

38 

37.86 

3.31 

37.84 

3.48 

37.83 

3.64 

37.81 

3.81 

38 

39 

38.85 

3.40 

38.84 

3.57 

38.82 

3.74 

38.80 

3.91 

39 

! 40 

39.85 

3.49 

39.83 

3.66 

39.82 

3.83 

39.80 

4.01 

40 

41 

40.84 

3.57 

40.83 

3.75 

40.81 

3.93 

40.79 

4.11 

41 

42 

41.84 

3.66 

41.82 

3.84 

41.81 

4.03 

41.79 

4.21 

42 

43 

42.84 

3.75 

42.82 

3.93 

42.80 

4.12 

42.78 

4.31 

43 

44 

43.83 

3.83 

43.82 

4.03 

43.80 

4.22 

43.78 

4.41 

44 

45 

44.83 

3.92 

44.81 

4.12 

44.79 

4.31 

44.77 

4.51 

45 

46 

45.82 

4.01 

45.81 

4.21 

45.79 

4.41 

45.77 

4.61 

46 

47 

46.82 

4.10 

46.80 

4.30 

46.78 

4.50 

46.76 

4.71 

47 

[| 48 

47.82 

4.18 

47.80 

4.39 

47.78 

4.60 

47.76 

4.81 

48 

II 49 

48.81 

4.27 

48.79 

4.48 

48.77 

4.70 

48.75 

4.91 

49 

1 50 

49.81 

4.36 

49.79 

4.58 

49.77 

4.79 

49.75 

, 5.01 

50 

Distance. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

« 

o 

85 Deg. 

841 Deg. 

84J Deg. 

84 £ Deg. 

- c 

aJ 

C/J 

• pH 

Q 

































































































































TRAVERSE TABLE. 


13 



G 

! ►— . 

U) 

r4- 

p 

o 

a 

5 Deg. 

5$ Deg. 

5i Deg. 

5$ Deg. 

1 Distance. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

51 

50.81 

4.44 

50.79 

4.67 

50.77 

4.89 

50.74 

5.11 

51 

52 

51.80 

4.53 

51.78 

4.76 

51.76 

4.98 

51.74 

5.21 

52 

53 

52.80 

4.62 

52.78 

4.85 

52.76 

5.08 

52.73 

5.31 

53 

54 

53.79 

4.71 

53.77 

4.94 

53.75 

5.18 

53.73 

5.41 

54 

55 

54.79 

4.79 

54.77 

5.03 

54.75 

5.27 

54.72 

5.51 

55 

50 

55.79 

4.88 

55.77 

5.12 

55.74 

5.37 

55.72 

5.61 

56 

57 

56.78 

4.97 

56.76 

5.22 

56.74' 

5.46 

56.71 

5.71 

57 

58 

57.78 

5.06 

57.76 

5.31 

57.73 

5.56 

57.71 

5.81 

58 

59 

58.78 

5.14 

58.75 

5.40 

58.73 

5.65 

58.70 

5.91 

59 

60 

59.77 

5.23 

59.75 

5.49 

59.72 

5.75 

59.70 

6.01 

60 

61 

60.77 

5.32 

60.74 

5.58 

60.72 

5.85 

60.69 

6.11 

61 

62 

61.76 

5.40 

61.74 

5.67 

61.71 

5.94 

61.69 

6.21 

62 

63 

62.76 

5.49 

62.74 

5.76 

62.71 

6.04 

62.68 

6.31 

63 

64 

63.76 

5.58 

63.73 

5.86 

63.71 

6.13 

63.68 

6.41 

64 

65 

64.75 

5.67 

64.73 

5.95 

64.70 

6.23 

64.67 

6.51 

65 

66 

65.75 

5.75 

65.72 

6.04 

65.70 

6.33 

65.67 

6.61 

66 

67 

66.75 

5.84 

66.72 

6.13 

66.69 

6.42 

66.66 

6.71 

67 

68 

67.74 

5.93 

67.71 

6.22 

67.69 

6.52 

67.66 

6.81 

68 

69 

68.74 

6.01 

68.71 

6.31 

68.68 

6.61 

68.65 

6.91 

69 

70 

69.73 

6.10 

69.71 

6.41 

69.68 

6.71 

69.65 

7.01 

70 

71 

70.73 

6.19 

70.70 

6.50 

70.67 

6.81 

70.64 

7.11 

71 

72 

71.73 

6.28 

71.70 

6.59 

71.67 

6.90 

71.64 

7.21 

72 

73 

72.72 

6.36 

72.69 

6.68 

72.66 

7.00 

72.63 

7.31 

73 

74 

73.72 

6.45 

73.69 

6.77 

73.66 

7.09 

73.63 

7.41 

74 

75 

74.71 

6.54 

74.69 

6.86 

74.65 

7.19 

74.62 

7.51 

75 

76 

75.71 

6.62 

75.68 

6.95 

75.65 

7.28 

75.62 

7.61 

76 

77 

76.71 

6.71 

76.68 

7.05 

76.65 

7.38 

76.61 

7.71 

77 

78 

77.70 

6.80 

77.67 

7.14 

77.64 

7.48 

77.61 

7.81 

78 

79 

78.70 

6.89 

78.67 

7.23 

78.64 

7.57 

78.60 

7.91 

79 

80 

79.70 

6.97 

79.66 

7.32 

79.63 

7.67 

.... _. . . 

79.60 

8.02 

80 

81 

80.69 

7.06 

80.66 

7.41 

80.63 

7.76 

80.59 

8.12 

81 

82 

81.69 

7.15 

81.66 

7.50 

81.62 

7.86 

81.59 

8.22 

82 

83 

82.68 

7.23 

82.65 

7.59 

82.62 

7.96 

82.58 

8.32 

83 

\ 84 

83.68 

7.32 

83.65 

7.69 

83.61 

8.05 

83.58 

8.42 

84 

85 

84.68 

7.41 

84.64 

7.78 

84.61 

8.15 

84.57 

8.52 

85 

86 

85.67 

7.50 

85.64 

7.87 

85.60 

8.24 

85.57 

8.62 

86 

87 

86.67 

7.58 

86.64 

7.96 

86.60 

8.34 

86.56 

8.72 

87 

88 

87.67 

7.67 

87.63 

8.05 

87.59 

8.43 

87.56 

8.82 

88 

89 

88.66 

7.76 

88.63 

8.14 

88.59 

8.53 

88.55 

8.92 

89 

90 

89.66 

7.84 

89.62 

8.24 

89.59 

8.63 

89.55 

9.02 

90 

91 

90.65 

7.93 

90.62 

8.33 

90.58 

8.72 

90.54 

9.12 

91 

92 

91.65 

8.02 

91.61 

8.42 

91.58 

8.82 

91.54 

9.22 

92 

i 93 

92.65 

8.IT 

92.61 

8.51 

92.57 

8.91 

92.53 

9.32 

93 

94 

93.64 

8.19 

93.61 

8.60 

93.57 

9.01 

93.53 

9.42 

94 

95 

94.64 

8.28 

94.60 

8.69 

94.56 

9.11 

94.52 

9.52 

95 

96 

95.63 

8.37 

95.60 

8.78 

95.56 

9.20 

95.52 

9.62 

96 

97 

96.63 

8.45 

96.59 

8.88 

96.55 

9.30 

96.51 

9.72 

97 

98 

97.63 

8.54 

97.59 

8.97 

97.55 

9.39 

97.51 

9.82 

98 

99 

98.62 

8.63 

98.59 

9.06 

98.54 

9.49 

98.50 

9.92 

99 

100 

99.62 

8.72 

99.58 

9.15 

99.54 

9.58 

99.50 

10.02 

100 

<u 

o 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

6 

o 

p 

CT5 

•+-> 

to 

Q 

85 Deg. 

84$ Deg. 

84 & Deg. 

84$ Deg. 

-*■-» i 

(11 

Q 


r 





















































































































TRAVERSE TABLE. 


1 Distance. 

6 Deg. 

Deg. 

6^ Deg. 

6f Deg. 

Distance. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

1 

0.99 

0.10 

0.99 

0.11 

0.99 

0.11 

0.99 

0.12 

1 

2 

1.99 

0.21 

1.99 

0.22 

1.99 

0.23 

1.99 

0.24 

2 

3 

2.98 

0.31 

2.98 

0.33 

2.98 

0.34 

2.98 

0.35 

3 

4 

3.98 

0.41 

3.98 

0.44 

3.97 

0.45 

3.97 

0.47 

4 

5 

4.97 

0.52 

4.97 

0.54 

4.97 

0.57 

4.97 

0.59 

5 

6 

5.97 

0.63 

5.96 

0.65 

5.96 

0.68 

5.96 

0.71 

6 

7 

6.96 

0.73 

6.96 

0.76 

6.96 

0.79 

6.95 

0.82 

7 

8 

7.96 

0.84 

7.95 

0.87 

7.95 

0.91 

7.94 

0.94 

8 

9 

8.95 

0.94 

8.95 

0.98 

8.94 

1.02 

8.94 

1.06 

9 

10 

9.95 

1.05 

9.94 

1.09 

9.94 

1.13 

9.93 

1.18 

10 

11 

10.94 

1.15 

10.93 

1.20 

10.93 

1.25 

10.92 

1.29 

11 

12 

11.93 

1.25 

11.93 

1.31 

11.92 

1.36 

11.92 

1.41 

12 

13 

12.93 

1.36 

12.92 

1.42 

12.92 

1.47 

12.91 

1.53 

13 

14 

13.92 

1.46 

13.92 

1.52 

13.91 

1.59 

13.90 

1.65 

14 

15 

14.92 

1.57 

14.91 

1.63 

14.90 

1.70 

14.90 

1.76 

15 

16 

15.91 

1.67 

15.90 

1.74 

15.90 

1.81 

15.89 

1.88 

16 

17 

16.91 

1.78 

16.90 

1.85 

16.89 

1.92 

16.88 

2.00 

17 

18 

17.90 

1.88 

17.89 

1.96 

17.88 

2.04 

17.88 

2.12 

18 

19 

18.90 

1.99 

18.89 

2.07 

18.88 

2.15 

18.87 

2.23 

19 

20 

19.89 

2.09 

19.88 

2.18 

19.87 

2.26 

19.86 

2.35 

20 

21 

20.88 

2.20 

20.88 

2.29 

20.87 

2.38 

20.85 

2.47 

21 

22 

21.88 

2.30 

21.87 

2.40 

21.86 

2.49 

21.85 

2.59 

22 

23 

22.87 

2.40 

22.86 

2.50 

22.85 

2.60 

22.84 

2.70 

23 

24 

23.87 

2.51 

23.86 

2.61 

23.85 

2.72 

23.83 

2.82 

24 

25 

24.86 

2.61 

24.85 

2.72 

24.84 

2.83 

24.83 

2.94 

25 

26 

25.86 

2.72 

25.85 

2.83 

25.83 

2.94 

25.82 

3.06 

26 

27 

26.85 

2.82 

26.84 

2.94 

26.83 

3.06 

26.81 

3.17 

27 

28 

27.85 

2.93 

27.83 

3.05 

27.82 

3.17 

27.81 

3.29 

28 

I 29 

28.84 

3.03 

28.83 

3.16 

28.81 

3.28 

28.80 

3.41 

29 

30 

29.84 

3.14 

29.82 

3.27 

29.81 

3.40 

29.79 

3.53 

30 

31 

30.83 

3.24 

30.82 

3.37 

30.80 

3.51 

30.79 

3.64 

31 

32 

31.82 

3.34 

31.81 

3.48 

31.79 

3.62 

31.78 

3.76 

32 

33 

32.82 

3.45 

32.80 

3.59 

32.79 

3.74 

32.77 

3.88 

33 

34 

33.81 

3.55 

33.80 

3.70 

33.78 

3.85 

33.76 

4.00 

34 

35 

34.81 

3.66 

34.79 

3.81 

34.78 

3.96 

34.76 

4.11 

35 

36 

35.80 

3.76 

35.79 

3.92 

35.77 

4.08 

35.75 

4.23 

36 

37 

36.80 

3.87 

36.78 

4.03 

36.76 

4.19. 

36.75 

4.35 

37 

38 

37.79 

3.97 

37.77 

4.14 

37.76 

4.30 

37.74 

4.47 

38 

39 

38.79 

4.08 

38.77 

4.25 

38.75 

4.41 

38.73 

4.58 

39 

40 

39.78 

4.18 

39.76 

4.35 

39.74 

4.53 

39.72 

4.70 

40 

41 

40.78 

4.29 

40.76 

4.46 

40.74 

4.64 

40.72 

4.82 

41 

42 

41.77 

4.39 

41.75 

4.57 

41.73 

4.76 

41.71 

4.94 

42 

43 

42.76 

4.49 

42.74 

4.68 

42.72 

4.87 

42.70 

5.05 

43 

44 

43.76 

4.60 

43.74 

4.79 

43.72 

4.98 

43.70 

5.17 

44 

45 

44.75 

4.70 

44.73 

4.90 

44.71 

5.09 

44.69 

5.29 

45 

46 

45.75 

4.81 

45.73 

5.01 

45.70 

5.21 

45.68 

5.41 

46 

47 

46.74 

4.91 

46.72 

5.12 

46.70 

5.32 

46.67 

5.52 

47 

48 

47.74 

5.02 

47.71 

5.23 

47.69 

5.43 

47.67 

5.64 

48 

49 

48.73 

5.12 

48.71 

5.34 

48.69 

5.55 

48.66 

5.76 

49 

50 

49.73 

5.23 

49.70 

5.44 

49.68 

5.66 

49.65 

5.88 

50 1 

Distance. 

Dep. | 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 1 

Lat. 

6 .! 

o 

£ 

d 1 

-*-» i 

1 1 ) 

• —H 1 

Q 

84 Deg. 

83$ Deg. 

83 h Deg. 

834 Deg. 


















































































TRAVERSE TABLE 


15 


) 


1 Distance. 

6 Deg. 

6| Deg. 

6i Deg. 

6| Deg. 

Distance. 

i 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

51 

50.72 

5.33 

50.70 

5.55 

50.67 

5.77 

50.65 

5.99 

51 

52 

51.72 

5.44 

51.69 

5.66 

51.67 

5.89 

51.64 

6.11 

52 

53 

52.71 

5.54 

52.68 

5.77 

52.66 

6.00 

52.63 

6.23 

53 

54 

53.70 

5.64 

53.68 

5.88 

53.65 

6.11 

53.63 

6.35 

54 

55 

54.70 

5.75 

54.67 

5.99 

54.65 

6.23 

54.62 

6.46 

55 

56 

55.69 

5.85 

55.67 

6.10 

55.64 

6.34 

55.61 

6.58 

56 

57 

56.69 

5.96 

56.66 

6.21 

56.63 

6.45 

56.60 

6.70 

57 

58 

57.68 

6.06 

57.66 

6.31 

57.63 

6.57 

57.60 

6.82 

58 

59 

58.68 

6.17 

58.65 

6.42 

58.62 

6.68 

58.59 

6.93 

59 

60 

59.67 

6.27 

59.64 

6.53 

59.61 

6.79 

59.58 

7.05 

60 

61 

60.67 

6.38 

60.64 

6.64 

60.61 

6.91 

60.58 

7.17 

61 

62 

61.66 

6.48 

61.63 

6.75 

61.60 

7.02 

61.57 

7.29 

62 

63 

62.65 

6.59 

62.63 

6.86 

62.60 

7.13 

62.56 

7.40 

63 

64 

63.65 

6.69 

63.62 

6.97 

63.59 

7.25 

63.56 

7.52 

64 

65 

64.64 

6.79 

64.61 

7.08 

64.58 

7.36 

64.55 

7.64 

65 

66 

65.64 

6.90 

65.61 

7.19 

65.58 

7.47 

65.54 

7.76 

66 

67 

66.63 

7.00 

66.60 

7.29 

66.57 

7.58 

66.54 

7.88 

67 

68 

67.63 

7.11 

67.60 

7.40 

67.56 

7.70 

67.53 

7.99 

68 

69 

68.62 

7.21 

68.59 

7.51 

68.56 

7.81 

68.52 

8.11 

69 

70 

69.62 

7.32 

69.58 

7.62 

69.55 

7.92 

69.51 

8.23 

70 

71 

70.61 

7.42 

70.58 

7.73 

70.54 

8.04 

70.51 

8.35 

71 

72 

71.61 

7.53 

71.57 

7.84 

71.54 

8.15 

71.50 

8.46 

72 

73 

72.60 

7.63 

72.57 

7.95 

72.53 

8.26 

72.49 

8.58 

73 

74 

73.59 

7.74 

73.56 

8.06 

73.52 

8.38 

73.49 

8.70 

74 

75 

74.59 

7.84 

74.55 

8.17 

74.52 

8.49 

74.48 

8.82 

75 

76 

75.58 

, 7.94 

75.55 

8.27 

75.51 

8.60 

75.47 

8.93 

76 

77 

76.58 

8.05 

76.54 

8.38 

76.51 

8.72 

76.47 

9.05 

77 

78 

77.57 

8.15 

77.54 

8.49 

77.50 

8.83 

77.46 

9.17 

78 

79 

78.57 

8.26 

78.53 

8.60 

78.49 

8.94 

78.45 

9.29 

79 

80 

79.56 

8.36 

79.53 

8.71 

79.49 

9.06 

79.45 

9.40 

80 

81 

80.56 

8.47 

80.52 

8.82 

80.48 

9.17 

80.44 

9.52 

81 : 

82 

81.55 

8.57 

81.51 

8.93 

81.47 

9.28 

81.43 

9.64 

82 

83 

82.55 

8.68 

82.51 

9.04 

82.47 

9.40 

82.42 

9.76 

83 

84 

83.54 

8.78 

83.50 

9.14 

83.46 

9.51 

83.42 

9.87 

84 

85 

84.53 

8.88 

84.50 

9.25 

84.45 

9.62 

84.41 

9.99 

85 

86 

85.53 

8.99 

85.49 

9.36 

85.45 

9.74 

85.40 

10.11 

86 

87 

86.52 

9.09 

86.48 

9.47 

86.44 

9.85 

86.40 

10.23 

87 

88 

87.52 

9.20 

87.48 

9.58 

87.43 

9.96 

87.39 

10.34 

88 

89 

88.51 

9.30 

88.47 

9.69 

88.43 

10.08 

88.38 

10.46 

89 

90 

89.51 

9.41 

89.47 

9.80 

89.42 

10.19 

89.38 

10.58 

90 

91 

90.50 

9.51 

90.46 

9.91 

90.42 

10.30 

90.37 

10.70 

91 

92. 

91.50 

9.62 

91.45 

10.02 

91.41 

10.41 

91.36 

10.81 

92 

93 

92.49 

9.72 

92.45 

10.12 

92.40 

10.53 

92.36 

10.93 

93 

94 

93.49 

9.83 

93.44 

10.23 

93.40 

10.64 

93.35 

11.05 

94 

95 

94.48 

9.93 

94.44 

10.34 

94.39 

10.75 

94.34 

11.17 

95 

96 

95.47 

10.03 

95.43 

10.45 

95.38 

10.87 

95.33 

11.28 

96 

97 

96.47 

10.14 

96.42 

10.56 

96.38 

10.98 

96.33 

11.40 

97 

98 

97.46 

10.24 

97.42 

10.67 

97.37 

11.09 

97.32 

11.52 

98 

99 

98.46 

10.35 

98.41 

10.78 

98.36 

11.21 

98.31 

11.64 

99 

100 

99.45 

10.45 

99.41 

10.89 

99.36 

11.32 

99.31 

11.75 

100 

> 

0) 

o 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

6 

o 

£ 

—* 

a 

-4-* 

C/3 

Q 

84 Deg. 

83f Deg. 

83£ Deg. 

83^ Beg. 

ct2 

C/i 

Q 

































































































































t 


](-, TRAVERSE TABLE. 


Distance. 

7 Dog. 

U Deg. 

U Deg. 

7f Deg. 

! Distance. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

1 

0.99 

0.12 

0.99 

0.13 

0.99 

0.13 

0.99 

0.13 

1 

2 

1.99 

0.24 

1.98 

0.25 

1.98 

0.26 

1.98 

0.27 

2 

3 

2.98 

0.37 

2.98 

0.38 

2.97 

0.39 

2.97 

0.40 

3 

4 

3.97 

0.49 

3.97 

0.50 

3.97 

0.52 

3.96 

0.54 

4 ; 

5 

4.96 

0.61 

4.96 

0.63 

4.96 

0.65 

4.95 

0.67 

5 

6 

5.96 

0.73 

5.95 

0.76 

5.95 

0.78 

5.95 

0.81 

6 

7 

6.95 

0.85 

6.94 

0.88 

6.94 

0.91 

6.94 

0.94 

7 

8 

7.94 

0.97 

7.94 

1.01 

7.93 

1.04 

7.93 

1.08 

8 

9 

8.93 

1.10 

8.93 

1.14 

8.92 

1.17 

8.92 

1.21 

9 ! 

10 

9.93 

1.22 

9.92 

1.26 

9.91 

1.31 

9.91 

1.35 

10 > 

11 

10.92 

1.34 1 

10.91 

1.39 

10.91 

1.44 

10.90 

1.48 

11 

12 

11.91 

1.46 | 

11.90 

1.51 

11.90 

1.57 

11.89 

1.62 

12 

13 

12.90 

1.58 

12.90 

1.64 

12.89 

1.70 

12.88 

1.75 

13 ; 

14 

13.90 

1.71 

13.89 

1.77 

13.88 

1.83 

13.87 

1.89 

14 : 

15 

14.89 

1.83 

14.88 

1.89 

14.87 

1.96 

14.86 

2.02 

15 : 

16 

15.88 

1.95 

15.87 

2.02 

15.86 

2.09 

15.85 

2.16 

16 

17 

16.87 

2.07 

16.86 

2.15 

16.85 

2.22 

16.84 

2.29 

17 

18 

17.87 

2.19 

17.86 

2.27 

17.85 

2.35 

17.84 

2.43 

18 

19 

18.86 

2.32 

18.85 

2.40 

18.84 

2.48 

18.83 

2.56 

19 

20 

19.85 

2.44 

19.84 

2.52 

19.83 

2.61 

19.82 

- 

2.70 

20 

21 

20.84 

2.56 

20.83 

2.65 

20.82 

2.74 

20.81 

2.83 

21 

22 

21.84 

2.68 

21.82 

2.78 

21.81 

2.87 

21.80 

2.97 

22 

23 

22.83 

2.80 

22.82 

2.90 

22.80 

3.00 

22.79 

3.10 

23 

24 

23.82 

2.92 

23 81 

3.03 

23.79 

3.13 

23.78 

3.24 

24 

25' 

24.81 

3.05 

24.80 

3.15 

24-79 

3.26 

24.77 

3.37 

25 

26 

25.81 

3.17 

25.79 

3.28 

25.78 

3.39 

25.76- 

3.51 

26 

27 

26.80 

3.29 

26.78 

3.41 

26.77 

3.52 

26.75 

3.64 

27 

28 

27.79 

3.41 

27.78 

3.53 

27.76 

3.65 

27.74 

3.78 

28 j 

29 

28.78 

3.53 

28.77 

3.66 

28.75 

3.79 

28.74 

3.91 

29 

30 

29.78 

3.66 

29.76 

• 3.79 

29.74 

3.92 

29.73 

4.05 

30j 

31 

30.77 

3.78 

30.75 

3.91 

30.73 

4.05 

30.72 

4.18 

31 

32 

31.76 

3.90 

31.74 

4.04 

31.73 

4.18 

31.71 

4.32 

32 

33 

32.75 

4.02 

32.74 

4.16 

32.72 

4.31 

32.70 

4.45 

33 

34 

33.75 

4.14 

33.73 

4.29 

33.71 

4.44 

33.69 

4.58 

34 

35 

34.74 

4.27 

34.72 

4.42 

34.70 

4.57 

34.68 

4.72 

35 

36 

35.73 

4.39 

35.71 

4.54 

35.69 

4.70 

35.67 

4.85 

36 

37 

36.72 

4.51 

36.70 

4.67 

36.68 

4.83 

36.66 

4.99 

37 

38 

37.72 

4.63 

37.70 

4.80 

37.67 

4.96 

37.65 

5.12 

38 

39 

38.71 

4.75 

38.69 

4.92 

38.67 

5.09 

38.64 

5.26 

39 

40 

39.70 

4.87 

39.68 

5.05 

39.66 

5.22 

39.63 

5.39 

40 

41 

40.70 

5.00 

40.67 

5.17 

40.65 

5.35 

i 40.63 

5.53 

41 

42 

41.69 

5.12 

41.66 

5.30 

41.64 

5.48 

41.62 

5.66 

42 

43 

42.68 

5.24 

42.66 

5.43 

42.63 

5.61 

I 42.61 

5.80 

43 

44 

43.67 

5.36 

43.65 

5.55 

43.62 

5.74 

43.60 

5.93 

44 

45 

44.67 

5.48 

! 44.64 

5.68 

44.62 

5.87 

44.59 

6.07 

45* 

46 

45.66 

5.61 

45.63 

5.81 

45.61 

6.00 

45.58 

6.20 

46 

47 

46.65 

5.73 

46.62 

5.93 

46.60 

6.13 

46.57 

6.34 

47 

48 

47.64 

5.85 

47.62 

6.06 

47.59 

6.27 

47.56 

6.47 

48 

49 

48.63 

5.97 

48.61 

6.18 

48.58 

6.40 

48.55 

6.61 

49 

50 

49.63 

6.09 

1 49.60 

\ 

6.31 

49.57 

6.53 

49.54 

6.74 

50 

| Distance. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Distance. 

83 Deg. 

82| Deg. 

i 

82£ Deg. 

824 Deg. 



















































































































TRAVERSE TABLE 


17 


D 

rr> 

P 

1 ^ 

7 Deg. 

U Deg. 

U Deg. 

7| Deg. 

C 

*—<. 

CD 

r-*- 

P 

i o 

1 ? 

| 

Lat. 

I - 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

p 

o 

(6 

51 

50.62 

6.22 

50.59 

6.44 

50.56 

6.66 

50.53 

6.88 

51 

: 52 

51.61 

6.34 

51.58 

6.56 

51.56 

6.79 

51.53 

7.01 

52 

53 

52.60 

6.46 

52.58 

6.69 

52.55 

6.92 

52.52 

7.15 

53 

j 54 

53.60 

6.58 

53.57 

6.81 

53.54 

7.05 

53.51 

7.28 

54 

55 

54.59 

6.70 

54.56 

6.94 

54.53 

7.18 

54.50 

7.42 

55 

56 

55.58 

6.82 

55.55 

7.07 

55.52 

7.31 

55.49 

7.55 

56 

57 

56.58 

6.95 

56.54 

7.19 

56.51 

7.44 

56.48 

7.69 

57 

58 

57.57 

7.07 

57.54 

7.32 

57.50 

7.57 

57.47 

7.82 

58 

t 59 

58.56 

7.19 

58.53 

7.45 

58.50 

7.70 

58.46 

7.96 

59 

60 

59.55 

7.31 

59.52 

7.57 

59.49 

7.83 

59.45 

8.09 

60 

61 

60.55 

7.43 

60.51 

7.70 

60.48 

7.96 

60.44 

8.23 

61 

62 

61.54 

7.56 

61.50 

7.82 

61.47 

8.09 

61.43 

8.36 

62 

63 

62.53 

7.68 

62.50 

7.95 

62.46 

8.22 

62.42 

8.50 

63 

64 

63.52 

7.80 

63.49 

8.08 

63.45 

8.35 

63.42 

8.63 

64 

65 

64.52 

7.92 

64.48 

8.20 

64.44 

8.48 

64.41 

8.77 

65 

66 

65.51 

8.04 

65.47 

8.33 

65.44 

8.61 

65.40 

8.90 

66 

67 

66.50 

8.17 

66.46 

8.46 

66.43 

8.75 

66.39 

9.04 

67 

68 

67.49 

8.29 

67.46 

8.58 

67.42 

8.88 

67.38 

9.17 

68 

69 

68.49 

8.41 

68.45 

8.71 

68.41 

9.01 

68.37 

9.30 

69 

70 

69.48 

8.53 

69.44 

8.83 

69.40 

9.14 

69.36 

9.44 

70 

71 

70.47 

8.65 

70.43 

8.96 

70.39 

9.27 

70.35 

9.57 

71 

72 

71.46 

8.77 

71.42 

9.09 

71.38 

9.40 

71.34 

9.71 

72 

73 

72.46 

8.90 

72.42 

9.21 

72.38 

9.53 

72.33 

9.84 

73 

74 

73.45 

9.02 

73.41 

9.34 

73.37 

9.66 

73.32 

9.98 

74 

75 

74.44 

9.14 

74.40 

9.46 

74.36 

9.79 

74.31 

10.11 

75 

76 

75.43 

9.26 

75.39 

9.59 

75.35 

9.92 

75.31 

10.25 

76 

: 77 

76.43 

9.38 

76.38 

9.72 

76.34 

10.05 

76.30 

10.38 

77 

78 

77.42 

9.51 

77.38 

9.84 

77.33 

10.18 

77.29 

10.52 

78 

79 

78.41 

9.63 

78.37 

9.97 

78.32 

10.31 

78.28 

10.65 

79 

80 

79.40 

9.75 

79.36 

10.10 

79.32 

10.44 

79.27 

10.79 

80 

81 

80.40 

9.87 

80.35 

10.22 

80.31 

10.57 

80.26 

1 0.92 

81 

82 

81.39 

9.99 

81.34 

10.35 

81.30 

10.70 

81.25 

11.06 

82 

83 

82.38 

10.12 

82.34 

10.47 

82.29 

10.83 

82.24 

11.19 

83 

84 

83.37 

10.24 

83.33 

10.60 

83.28 

10.96 

83.23 

11.33 

84 

85 

84.37 

10.36 

84.32 

10.73 

84.27 

11.09 

84.22 

11.46 

85 

86 

85.36 

10.48 

85.31 

10.85 

85.26 

11.23 

85.21 

11.60 

86 

87 

86.35 

10.60 

86.30 

10.98 

86.26 

11.36 

86.21 

11.73 

87 

88 

87.34 

10.72 

87.30 

11.11 

87.25 

11.49 

87.20 

11.87 

88 

89 

88.34 

10.85 

88.29 

11.23 

88.24 

11.62 

88.19 

12.00 

89 

90 

89.33 

10.97 

1 

89.28 

11.36 

89.23 

11.75 

89.18 

12.14 

90 

91 

90.32 

11.09 

90.27 

11.48 

90.22 

11.88 

90.17 

12.27 

91 

92 

91.31 

11.21 

91.26 

11.61 

91.21 

12.01 

91.16 

12.41 

92 

93 

92.31 

11.33 

92.26 

11.74 

92.20 

12.14 

92.15 

12.54 

93 

94 

93.30 

11.46 

93.25 

11.86 

93.20 

12.27 

93.14 

12.68 

94 

95 

94.29 

11.58 

94.24 

11.99 

94.19 

12.40 

94.13 

12.81 

95 

96 

95.28 

11.70 

95.23 

12.12 

95.18 

12.53 

95.12 

12.95 

96 

97 

96.28 

11.82 

96.22 

12.24 

96.17 

12.66 

96.11 

13.08 

97 

98 

97.27 

11.94 

97.22 

12.37 

97.16 

12.79 

97.10 

13.22 

98 

99 

98.26 

12.07 

98.21 

12.49 

98.15 

12.92 

98.10 

13.35 

99 

100 

99.25 

12.19 

99.20 

12.62 

99.14 

13.05 

99.09 

13.49 

00 

6 

o 

Dep. 

Lat. 

Dep. i 

Lat. 

Dep. 

Lat. 

Dep. | 

Lat. 

• 

<u 

o 

a 

r/5 

3 

83 Deg. 

i 

f 

82} Deg. 

82} Deg. 

i 

82} Deg. 

i 

flS 

■w 

CD 

'A 


c 



















































































































]8 


TRAVERSE TABLE. 



t 





































































































































TRAVERSE TABLE 


19 


d 

N • 

rr. 

S 

s 

o 

(T> 

: 1 • 

8 Deg. 

8\ Deg. 

8 £ Deg. 

8f Deg. 

| Distance. 

Lat. 

| Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

1 51 

50.50 

7.10 

50.47 

7.32 

50.44 

7.54 

50.41 

7.76 

51 

52 

51.49 

7.24 

51.46 

7.46 

51.43 

7.69 

51.39 

7.91 

52 | 

53 

52.48 

7.38 

52.45 

7.61 

52.42 

7.83 

52.38 

8.06 

53 I 

i 54 

53.47 

7.52 

53.44 

7.75 

53.41 

7.98 

53.37 

8.21 

54 | 

55 

54.46 

7.65 

54.43 

7.89 

1 54.40 

8.13 

54.36 

8.37 

55 1 

56 

55.46 

7.79 

55.42 

8.04 

55.38 

8.28 

55.35 

8.52 

56 

57 

56.45 

7.93 

56.41 

8.18 

56.37 

8.43 

56.34 

8.67 

57 

‘ 58 

57.44 

8.07 

57.40 

8.32 

57.36 

8.57 

57.32 

8.82 

58 

59 

58.43 

8.21 

58.39 

8.47 

58.35 

8.72 

58.31 

8.98 

59 

60 

59.42 

8.35 

59.38 

8.61 

59.34 

8.87 

59.30 

9.13 

60 

61 

60.41 

8.49 

60.37 

8.75 

60.33 

9.02 

60.29 

9.28 

61 

62 

61.40 

8.63 

61.36 

8.90 

61.32 

9.16 

61.28 

9.43 

62 

63 

62.39 

8.77 

62.35 

9.04 

62.31 

9.31 

62.27 

9.58 

63 

64 

63.38 

8.91 

63.34 

9.18 

63.30 

9.46 

63.26 

9.74 

64 

65 

64.37 

9.05 

64.33 

9.33 

64.29 

9.61 

64.24 

9.89 

65 

66 

65.36 

9.19 

65.32 

9.47 

65.28 

9.76 

65.23 

10.04 

66 

67 

66.35 

9.32 

66.31 

9.61 

66.26 

9.90 

66.22 

10.19 

67 

68 

67.34 

9.46 

67.30 

9.76 

67.25 

10.05 

67.21 

10.34 

68 

69 

68.33 

9.60 

68.29 

9.90 

68.24 

10.20 

68.20 

10.50 

69 

70 

69.32 

9.74 

69.28 

10.04 

69.23 

10.35 

69.19 

10.65 

70 

71 

70.31 

9.88 

70.27 

10.19 

70.22 

10.49 

70.17 

10.80 

71 

72 

71.30 

10.02 

71.25 

10.33 

71.21 

10.64 

71.16 

10.95 

72 

73 

72.29 

10.16 

72.24 

10.47 

72.20 

10.79 

72.15 

11.10 

73 

74 

73.28 

10.30 

73.23 

10.62 

73.19 

10.94 

73.14 

11.26 

74 

75 

74.27 

10.44 

74.22 

10.76 

74.18 

11.09 

74.13 

11.41 

75 

76 

75.26 

10.58 

75.21 

10.91 

75.17 

11.23 

75.12 

11.56 

76 

77 

76.25 

10.72 

76.20 

11.05 

76.15 

11.38 

76.10 

11.71 

77 

78 

77.24 

10.86 

77.19 

11.19 

77.14 

11.53 

77.09 

11.87 

78 

79 

78.23 

10.99 

78.18 

11.34 

78.13 

11.68 

78.08 

12.02 

79 

80 

79.22 

11.13 

79.17 

11.48 

79.12 

11.82 

79.07 

12.17 

80 

81 

80.21 

11.27 

80.16 

11.62 

80.11 

11.97 

80.06 

12.32 

81 

82 

81.20 

11.41 

81.15 

11.77 

81.10 

12.12 

81.05 

12.47 

82 

83 

82.19 

11.55 

82.14 

11.91 

82.09 

12.27 

82.03 

12.63 

83 

84 

83.13 

11.69 

83.13 

12.05 

83.08 

12.42 

83.02 

12.78 

84 

85 

84.17 

11.83 

84.12 

12.20 

, 84.07 

12.56 

84.01 

12.93 

85 

86 

85.16 

11.97 

85.11 

12.34 

85.06 

12.71 

85.00 

13.08 

86 

87 

86.15 

12.11 

86.10 

12.48 

86.04 

12.86 

85.99 

13.23 

87 

88 

87.14 

12.25 

87.09 

12.63 

87.03 

13.01 

86.98 

13.39 

88 

89 

88.13 

12.39 

88.08 

12.77 

88.02 

13.16 

87.96 

13.54 

89 

90 

89.12 

12.53 

89.07 

12.91 

89.01 

13.30 

88.95 

13.69 

90 

91 

90.11 

12.66 

90.06 

13.06 

90.00 

13.45 

89.94 

13.84 

91 

92 

91.10 

12.80 

91.05 

13.20 

90.99 

13.60 

90.93 

14.00 

92 

93 

92.09 

12.94 

92.04 

13.34 

91.98 

13.75 

91.92 

14.15 

93 

94 

93.09 

13.08 

93.03 

13.49 

92.97 

13.89 

92.91 

14.30 

94 

95 

94.08 

13.22 

94.02 

13.63 

93.96 

14.04 

93.89 

14.45 

95 

96 

95.07 

13.36 

95.01 

13.78 

94.95 

14.19 

94.88 

14.60 

96 

97 

96.06 

13.50 

96.00 

13.92 1 

95.93 

14.34 

95.87 

14.76 

97 

98 

97.05 

13.64 

96.99 

14.06 

96.92 

14.49 

96.86 

14.91 

98 

99 

98.04 

13.78 

97.98 

14.21 

97.91 

14. G3 

97.85 

15.06 

99 

100 

99.03 

13.92 

98.97 

14.35 | 

98.90 

14.78 

98.84 

15.21 

100 

_ 

1 

<0 

o 

Dep. J 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

aJ 

o 

5 
■*-> 
tn 
• *■•< 

82 Deg. j 

• 

81f Deg. 

| 

81 i Deg. 

8H Deg. 

1 

1 

c 





























































































































20 


TRAVERSE TABLE 


c 

!»' 

rt- 

V 

o 

o 

» 

9 Deg. 

9i Deg. 

9$ Deg. 

9| Deg. 

Distance. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

1 

0.99 

0.16 

0.99 

0.16 

0.99 

0*.17 

0.99 

0.17 

1 

2 

1.98 

0.31 

1.97 

0.32 

1.97 

0.33 

1.97 

0.34 

2 

3 

2.96 

0.47 

2.96 

0.48 

2.96 

0.50 

2.96 

0.51 

3 

4 

3.95 

0.63 

3.95 

0.64 

3.95 

0.66 

3.94 

0.68 

4 : 

5 

4.94 

0.78 

4.93 

0.80 

4.93 

0.83 

4.93 

0.85 

5 

6 

5.93 

0.94 

5.92 

0.96 

5.92 

0.99 

5.91 

1.02 

6 

7 

6.91 

1.10 

6.91 

1.13 

6.90 

1.16 

6.90 

1.19 

IT* 

i l 

8 

7.90 

1.25 

7.90 

1.29 

7.89 

1.32 

7.88 

1.35 

8 ; 

9 

8.89 

1.41 

8.88 

1.45 

8.88 

1.49 

8.87 

1.52 

9 

10 

9.88 

1.56 

9.87 

1.61 

9.86 

1.65 

9.86 

1.69 

10 

11 

10.86 

1.72 

10.86 

1.77 

10.85 

1.82 

10.84 

1.86 

11 | 

12 

11.85 

1.88 

11.84 

1.93 

11.84 

1.98 

11.83 

2.03 

121 

13 

12.84 

2.03 

12.83 

2.09 

12.82 

2.15 

12.81 

2.20 

13 1 

14 

13.83 

2.19 

13.82 

2.25 

13.81 

2.31 

13.80 

2.37 

14 1 

15 

14.82 

2.35 

14.80 

2.41 

14.79 

2.48 

14.78 

2.54 

15 

16 

15.80 

2.50 

15.79 

2.57 

15.78 

2.64 

15.77 

2.71 

16 

17 

16.79 

2.66 

16.78 

2.73 

16.77 

2.81 

16.75 

2.88 

17 

18 

17.78 

2.82 

17.77 

2.89 

17.75 

2.97 

17.74 

3.05 

18 

19 

18.77 

2.97 

18.75 

3.05 

18.74 

3.14 

18.73 

3.22 

19 

20 

19.75 

3.13 

19.74 

3.21 

19.73 

3.30 

19.71 

3.39 

20 

21 

20.74 

3.29 

20.73 

3.38 

20.71 

3.47 

20.70 

3.56 

21 

22 

21.73 

3.44 

21.71 

3.54 

21.70 

3.63 

21.68 

3.73 

22 

23 

22.72 

3.60 

22.70 

3.70 

22.68 

3.80 

22.67 

3.90 

23 

24 

23.70 

3.75 

23.69 

3.86 

23.67 

3.96 

23.65 

4.06 

24 

25 

24.69 

3.91 

24.67 

4.02 

24.66 

4.13 

24.64 

4.23 

25 

26 

25.68 

4.07 

25.66 

4.18 

25.64 

4.29 

25.62 

4.40 

26 

27 

26.67 

4.22 

26.65 

4.34 

26.63 

4.46 

26.61 

4.57 

27 

28 

27.66 

4.38 

27.64 

4.50 

27.62 

4.62 

27.60 

4.74 

28 

29 

28.64 

4.54 

28.62 

4.66 

28.60 

4.79 

28.58 

4.91 

29 

30 

29.63 

4.69 

29.61 

4.82 

29.59 

4.95 

29.57 

5.08 

30 

31 

30.62 

4.85 

30.60 

4.98 

30.57 

5.12 

30.55 

5.25 

31 

32 

31.61 

5.01 

31.58 

5.14 

31.56 

5.28 

31.54 

5.42 

32 

33 

32.59 

5.16 

32.57 

5.30 

32.55 

5.45 

32.52 

5.59 

33 

34 

33.58 

5.32 

33.56 

5.47 

33.53 

5.61 

33.51 

5.76 

34 

35 

34.57 

5.48 

34.54 

5.63 

34.52 

5.78 

34.49 

5.93 

35 

36 

35.56 

5.63 

35.53 

5.79 

35.51 

5.94 

35.48 

6.10 

36 

37 

36.54 

5.79 

36.52 

5.95 

36.49 

6.11 

36.47 

6.27 

37 

33 

37.53 

5.94 

37.51 

6.11 

37.48 

6.27 

37.45 

6.44 

38 

39 

38.52 

6.10 

38.49 

6.27 

38.47 

6.44 

38.44 

6.60 

39 

40 

39.51 

6.26 

39.48 

6.43 

39.45 

6.60 

39.42 

6.77 

40 1 

41 

40.50 

6.41 

40.47 

6.59 

40.44 

6.77 

40.41 

6.94 

41 

42 

41.48 

6.57 

41.45 

6.75 

41.42 

6.92 

41.39 

7.11 

42 

43 

42.47 

6.73 

42.44 

6.91 

42.41 

7.10 

42.38 

7.28 

43 

44 

43.46 

6.88 

43.43 

7.07 

43.40 

7.26 

43.36 

7.45 

44 

45 

44.45 

7.04 

44.41 

7.23 

44.38 

7.43 

44.35 

7.62 

45 

46 

45.43 

7.20 

45.40 

7.39 

45.37 

7.59 

45.34 

7.79 

46 

47 

46.42 

7.35 

46.39 

7.55 

46.36 

7.76 

46.32 

7.96 

47 

48 

47.41 

7.51 

47.38 

7.72 

47.34 

7.92 

47.31 

8.13 

48 

49 

48.40 

7.67 

48.36 

7.88 

48.33 

8.09 

48.29 

8.30 

49 

50 

49.38 

7.82 

49.35 

8.04 

49.32 

8.25 

49.28 

8.47 

50 

<£ 

o 

r* 

CtJ 

<z> 

* •*< 

Q 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

<u 

o 

c 

1 

81 Deg. 

80| Deg. 

80£ Deg. 

80$ Deg. 

























































































TRAVERSE TABLE 


21 


o 

U) ’ 

r-»- 

S» 

3 

O 

(6 

9 Deg. 

i 

94 Deg. 

94 Deg. 

9} Deg. 

Distance. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

51 

50.37 

7.98 

50.34 

8.20 

50.30 

8.42 

50.26 

8.64 

51 

52 

51.36 

8.13 

51.32 

8.36 

51.29 

8.58 

51.25 

8.81 

52 

! 53 

52.35 

8.29 

52.31 

8.52 

52.27 

8.75 

52.23 

8.98 

53 

54 

53.34 

8.45 

53.30 

8.68 

53.26 

8.91 

53.22 

9.14 

54 

55 

54.32 

8.60 

54.28 

8.84 

54.25 

9.08 

54.21 

9.31 

55 

| 56 

55.31 

8.76 

55.27 

9.00 

55.23 

9.24 

55.19 

9.48 

56 

f 57 

56.30 

8.92 

56.26 

9.16 

56.22 

9.41 

56.18 

9.65 

57 

58 

57.29 

9.07 

57.25 

9.32 

57.20 

9.57 

57.16 

9.82 

58 

59 

58.27 

9.23 

58.23 

9.48 

58.19 

9.74 

58.15 

9.99 

59 

; 60 

59.26 

9.39 

59.22 

9.64 

59.18 

9.90 

59.13 

10.16 

60 

61 

60.25 

9.54 

60.21 

9.81 

60.16 

10.07 

60.12 

10.33 

61 

62 

61.24 

9.70 

61.19 

9.97 

61.15 

10.23 

61.10 

10.50 

62 

63 

62.22 

9.86 

62.18 

10.13 

62.14 

10.40 

62.09 

10.67 

63 

64 

63.21 

10.01 

■ 63.17 

10.29 

63.12 

10.56 

63.08 

10.84 

64 

65 

64.20 

10.17 

64.15 

10.45 

64.11 

10.73 

64.06 

11.01 

65 

66 

65.19 

10.32 

65.14 

10.61 

65.09 

10.89 

65.05 

11.18 

66 

67 

66.18 

10.48 

66.13 

10.77 

66.08 

11.06 

66.03 

11.35 

67 

68 

67.16 

10.64 

67.12 

10.93 

67.07 

11.22 

67.02 

11.52 

68 

69 

68.15 

10.79 

! 68.10 

11.09 

68.05 

11.39 

68.00 

11.69 

69 

, 70 

69.14 

10.95 

69.09 

11.25 

69.04 

11.55 

68.99 

11.85 

70 

71 

70.13 

11.11 

70.08 

11.41 

70.03 

11.72 

69.97 

12.02 

71 

72 

71.11 

11.26 

71.06 

11.57 

71.01 

11.88 

70.96 

12.19 

72 

73 

72.10 

11.42 

72.05 

11.73 

72.00 

12.05 

71.95 

12.36 

73 

74 

73.09 

11.58 

73.04 

11.89 

72.99 

12.21 

72.93 

12.53 

74 

* 75 

74.08 

11.73 

74.02 

12.06 

73.97 

12.38 

73.92 

12.70 

75 

76 

75.06 

11.89 

75.01 

12.22 

74.96 

12.54 

74.90 

12.87 

76 

77 

76.05 

12.05 

76.00 

12.38 

75.94 

12.71 

75.89 

13.04 

/ l ! 

78 

77.04 

12.20 

76.99 

12.54 

76.93 

12.87 

76.87 

13.21 

78 

79 

78.03 

12.36 

77.97 

12.70 

77.92 

13.04 

77.86 

13.38 

79 

80 

79.02 

12.51 

78.96 

12.86 

78.90 

13.20 

78.84 

13.55 

80 

81 

80.00 

12.67 

79.95 

13.02 

79.89 

13.37 

79.83 

13.72 

81 

82 

80.99 

12.83 

80.93 

13.18 

80.88 

13.53 

80.82 

13.89 

82 

83 

81.98 

12.98 

81.92 

13.34 

81.86 

13.70 

81.80 

14.06 

83 

84 

82.97 

13.14 

82.91 

13.50 

82.85 

13.86 

82.79 

14.23 

84 

85 

83.95 

13.30 

83.89 

13.66 

83.83 

14.03 

83.77 

14.39 

85 

86 

84.94 

13.45 

84.88 

13.32 

84.82 

14.19 

84.76 

14.56 

86 

87 

85.93 

13.61 

85.87 

13.98 

85.81 

14.36 

85.74 

14.73 

87 

88 

86.92 

13.77 

86.86 

14.15 

86.79 

14.52 

86.73 

14.90 

88 

89 

87.90 

13.92 

87.84 

14.31 

87.78 

14.69 

87.71 

15.07 

89 

90 

88.89 

14.08 

88.83 

14.47 

88.77 

14.85 

88.70 

15.24 

90 

91 

89.88 

14.24 

89.82 

14.63 

89.75 

15.02 

89.69 

15.41 

91 

92 

90.87 

14.39 

90.80 

14.79 

90.74 

15.18 

90.67 

15.58 

92 

93 

91.86 

14.55 

91.79 

14.95 

91.72 

15.35 

91.66 

15.75 

93 

94 

92.84 

14.70 

92.78 

15.11 

92.71 

15.51 

92.64 

15.92 

94 

95 

93.83 

14.86 

93.76 

15.27 

93.70 

15.68 

93.63 

16.09 

95 

96 

94.82 

15.02 

94.75 

15.43 

94.68 

15.84 

94.61 

16.26 

96 

97 

95.81 

15.17 

95.74 

15.59 

95.67 

16.01 

95.60 

16.43 

97 

98 

96.79 

15.33 

96.73 

15.75 

96.66 

16.17 

96.58 

16.60 

98 

99 

97.78 

15.49 

97.71 

15.91 

97.64 

16.34 

97.57 

16.77 

99 

100 

98.77 

15.64 

98.70 

16.07 

98.63 

16.50 

98.56 

16.93 

100 

aJ 

o 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 1 

Lat. 

Dep. 

Lat. 

fl) 

o 

c 

od 

-*-> 

(/j 

Q 

81 Deg. j 

80| Deg. 

804 Deg. 

804 Deg. 

c t 

V) 

• 

Q 






































































































22 


TRAVERSE TABLE 


Distance. 

10 Deg. 

10} Deg. 

10* Deg. 

10| Deg. 

1 Distance. 

Lat. | 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

1 

0.98 

0.17 

0.98 

0.18 

0.98 

0.18 

0.98 

0.19 

1 

2 

1.97 

0.35 

1.97 

0.36 

1.97 

0.36 

1.96 

0.37 

2 

3 

2.95 

0.52 

2.95 

0.53 

2.95 

0.55 

2.95 

0.56 

3 

4 

3.94 

0.69 

3.94 

0.71 

3.93 

0.73 

3.93 

0.75 

4 

5 

4.92 

0.87 

4.92 

0.89 

4.92 

0.91 

4.91 

0.93 

5 

6 

5.91 

1.04 

5.90 

1.07 

5.90 

1.09 

5.89 

1.12 

6 

7 

6.89 

1.22 

6.89 

1.25 

6.88 

1.28 

6.88 

1.31 

i 

8 

7.88 

1.39 

7.87 

1.42 

7.87 

1.46 

7.86 

1.49 

8 

9 

8.86 

1.56 

8.86 

1.60 

8.85 

1.64 

8.84 

1.68 

9 

10 

9.85 

1.74 

9.84 

1.78 

9.83 

1.82 

9.82 

1.87 

10 

11 

10.83 

1.91 

10.82 

1.96 

10.82 

2.00 

10.81 

2.05 

11 

12 

11.82 

2.08 

11.81 

2.14 

11.80 

2.19 

11.79 

2.24 

12 

13 

12.80 

2.26 

12.79 

2.31 

12.78 

2.37 

12.77 

2.42 

13 

14 

13.79 

2.43 

13.78 

2.49 

13.77 

2.55 

13.75 

2.61 

14 

15 

14.77 

2.60 

14.76 

2.67 

14.75 

2.73 

14.74 

2.80 

15 

16 

15.76 

2.78 

15.74 

2.85 

15.73 

2.92 

15.72 

2.98 

16 

17 

16.74 

2.95 

16.73 

3.03 

16.72 

3.10 

16.70 

3.17 

17 

18 

17.73 

3.13 

17.71 

3.20 

17.70 

3.28 

17.68 

3.36 

18 

19 

18.71 

3.30 

18.70 

3.38 

18.68 

3.46 

18.67 

3.54 

19 

20 

19.70 

3.47 

19.68 

3.56 

19.67 

3.64 

19.65 

3.73 

20 

21 

20.68 

3.65 

20.66 

3.74 

20.65 

3.83 

20.63 

3.92 

21 

22 

21.67 

3.82 

21.65 

3.91 

21.63 

4.01 

21.61 

4.10 

22 

23 

22.65 

3.99 

22.63 

4.09 

22.61 

4.19 

22.60 

4.29 

23 

24 

23.64 

4.17 

23.62 

4.27 

23.60 

4.37 

23.58 

4.48 

24 

25 

24.62 

4.34 

24.60 

4.45 

24.58 

4.56 

24.56 

4.66 

25 

26 

25.61 

4.51 

25.59 

4.63 

25.56 

4.74 

25.54 

4.85 

26 

27 

26.59 

4.69 

26.57 

4.80 

26.55 

4.92 

26.53 

5.04 

27 

28 

27.57 

4.86 

27.55 

4.98 

27.53 

5.10 

27.51 

5.22 

28 

29 

28.56 

5.04 

28.54 

5.16 

28.51 

5.28 

28.49 

5.41 

29 

30 

29.54 

5.21 

29.52 

5.34 

29.50 

5.47 

29.47 

5.60 

30 

31 

30.53 

5.38 

30.51 

5.52 

30.48 

5.65 

30.46 

5.78 

31 

32 

31.51 

5.56 

31.49 

5.69 

31.46 

5.83 

31.44 

5.97 

32 

33 

32.50 

5.73 

32.47 

5.87 

32.45 

6.01 

32.42 

6.16 

33 

34 

33.48 

5.90 

33.46 

6.05 

33.43 

6.20 

33.40 

6.34 

34 

35 

34.47 

6.08 

34.44 

6.23 

34.41 

6.38 

34.39 

6.53 

35 

36 

35.45 

6.25 

35.43 

6.41 

35.40 

6.56 

35.37 

6.71 

36 

37 

36.44 

6.42 

36.41 

6.58 

36.38 

6.74 

36.35 

6.90 

37 

38 

37.42 

6.60 

37.39 

6.76 

37.36 

6.92 

37.33 

7.09 

38 

39 

38.41 

6.77 

38.38 

6.94 

38.35 

7.11 

38.32 

7.27 

39 

40 

39.39 

6.95 

39.36 

7.12 

39.33 

7.29 

39.30 

7.46 

40 

41 

40.38 

7.12 

40.35 

7.30 

40.31 

7.47 

40.28 

7.65 

41 

42 

41.36 

7.29 

41.33 

7.47 

41.30 

7.65 

41.26 

7.83 

42 

, 43 

42.35 

7.47 

42.31 

7.65 

42.28 

7.84 

42.25 

8.02 

43 

44 

43.33 

7.64 

43.30 

7.83 

43.26 

8.02 

43.23 

8.21 

44 

45 

44.32 

7.81 

44.28 

8.01 

44.25 

8.20 

44.21 

8.39 

45 

46 

45.30 

7.99 

45.27 

8.19 

45.23 

8.38 

45.19 

8.58 

46 

47 

46.29 

8.16 

46.25 

8.36 

46.21 

8.57 

46.18 

8.77 

47 

48 

47.27 

8.34 

47.23 

8.54 

47.20 

8.75 

47.16 

8.95 

48 

49 

48.26 

8.51 

48.22 

8.72 

48.18 

8.93 

48.14 

9 14 

49 

50 

49.24 

8.68 

49.20 

8.90 

49.16 

9.11 

49.12 

9.33 

50 

Distance. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Distance. 

80 Deg. 

i m D e g . 

79* Deg. 

79} Deg. 



























































































































TRAVERSE TABLE 


5 

rjj 

£ 

10 Deg. 

10* 

Deg. 

10* 

De°* 

10| 

Deg. 

s 

in 

r~f~ 

P 

o 

! o 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

o 

CD 

1 3 ^ 

50.23 

8.86 

50.19 

9.08 

50.15 

9.29 

50.10 

9.51 

51 

f 52 

51.21 

9.03 

51.17 

9.25 

51.13 

9.48 

51.09 

9.70 

52 

! 53 

52.19 

9.20 

52.15 

9.43 

52.11 

9.66 

52.07 

9.89 

53 

. 54 

53.18 

9.38 

53.14 

9.61 

53.10 

9.84 

53.05 

10.07 

54 

55 

54.16 

9.55 

54.12 

9.79 

54.08 

10.02 

54.03 

10.26 

55 

56 

55.15 

9.72 

55.11 

9.96 

55.06 

10.21 

55.02 

10.45 

56 

57 

56.13 

9.90 

56.09 

10.14 

56.05 

10.39 

56.00 

10.63 

57 

! 58 

57.12 

10.07 

57.07 

10.32 

57.03 

10.57 

56.98 

10.82 

58 

59 

58.10 

10.25 

58.06 

10.50 

58.01 

10.75 

57.96 

11.00 

59 

60 

59.09 

10.42 

59.04 

10.68 

59.00 

10.93 

58.95 

11.19 

60 

61 

60.07 

10.59 

60.03 

10.85 

59.98 

11.12 

59.93 

11.38 

61 

62 

61.06 

10.77 

61.01 

11.03 

60.96 

11.30 

60.91 

11.56 

62 

63 

62.04 

10.94 

61.99 

11.21 

61.95 

11.48 

61.89 

11.75 

63 

64 

63.03 

11.11 

62.98 

11.39 

62.93 

11.66 

62.88 

11.94 

64 

65 

64.01 

11.29 

63.96 

11.57 

63.91 

11.85 

63.86 

12.12 

65 

66 

65.00 

11.46 

64.95 

11.74 

64.89 

12.03 

64.84 

12.31 

66 

67 

65.98 

11.63 

65.93 

11.92 

65.88 

12.21 

65.82 

12.50 

67 

68 

66.97 

11.81 

66.91 

12.10 

66.86 

12.39 

66.81 

12.68 

68 

69 

67.95 

1*.98 

67.90 

12.28 

67.84 

12.57 

67.79 

12.87 

69 

70 

68.94 

12.16 

68.88 

12.46 

68.83 

12.76 

68.77 

13.06 

70 

71 

69.92 

12.33 

69.87 

12.63 

69.81 

12.94 

69.75 

13.24 

71 

72 

70.91 

12.50 

70.85 

12.81 

70.79 

13.12 

70.74 

13.43 

72 

78 

71.89 

12.68 

71.83 

12.99 

71.78 

13.30 

71.72 

13.62 

73 

74 

72.88 

12.85 

72.82 

13.17 

72.76 

13.49 

72.70 

13.80 

74 

75 

73.86 

13.02 

73.80 

13.35 

73.74 

13.67 

73.68 

13.99 

75 

76 

74.85 

13.20 

74.79 

13.52 

74.73 

13.85 

74.67 

14.18 

76 

77 

75.83 

13.37 

75.77 

13.70 

75.71 

14.03 

7.5.65 

14.36 

77 

78 

76.82 

13.54 

76.76 

13.88 

76.69 

14.21 

76.63 

14.55 

78 

79 

77.80 

13.72 

77.74 

14.06 

77.08 

14.40 

77.61 

14.74 

79 

80 

78.78 

13.89 

78.72 

14.24 

78.66 

14.58 

78.60 

14.92 

80 

81 

79.77 

14.07 

79.71 

14.41 

79.64 

14.76 

79.58 

15.11 

81 

82 

80.75 

14.24 

80.69 

14.59 

80.63 

14.94 

80.56 

15.29 

82 

83 

81.74 

14.41 

81.68 

14.77 

81.61 

15.13 

81.54 

15.48 

83 

84 

82.72 

14.59 

82.66 

14.95 

82.59 

15.31 

82.53 

15.67 

84 

85 

83.71 

14.76 

83.64 

15.13 

83.58 

15.49 

83.51 

15.85 

85 

86 

84.69 

14.93 

84.63 

15.30 

84.56 

15.67 

84.49 

16.04 

86 

[ 87 

85.68 

15.11 

85.61 

15.48 

85.54 

15.85 

85.47 

16.23 

87 

| 88 

86.66 

15.28 

86.60 

15.66 

86.53 

16.04 

86.46 

16.41 

88 

f 89 

87.65 

15.45 

87.58 

15.84 

87.51 

16.22 

87.44 

16.60 

89 

90 

88.63 

15.63 

88.56 

16.01 

88.49 

16.40 

88.42 

16.79 

90 

91 

89.62 

15.80 

89.55 

16.19 

89.48 

16.58 

89.40 

16.97 

91 1 

92 

90.60 

15.98 

90.53 

16.37 

90.46 

16.77 

90.39 

17.16 

92 

93 

91.59 

16.15 

91.52 

16.55 

91.44 

16.95 

91.37 

17.35 

93 

94 

92.57 

16.32 

92.50 

16.73 

92.43 

17.13 

92.35 

17.53 

94 

95 

93.56 

16.50 

93.48 

16.90 

93.41 

17.31 

93.33 

17.72 

95 

96 

94.54 

16.67 

94.47 

17.08 

94.39 

17.49 

94.32 

17.91 

96 

97 

95.53 

16.84 

95.45 

17.26 

95.38 

17.68 

95.30 

18.09 

97 

98 

96.51 

17.02 

96.44 

17.44 

96.36 

17.86 

96.28 

18.28 

98 

99 

97.50 

17.19 

97.42 

17.62 

97.34 

18.04 

97.26 

18.47 

99 

100 

98.48 

17.36 

98.40 

17.79 

98.33 

18.22 

98.25 

18.65 

100 

6 

o 

Dep. 1 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lcit* 

oJ 

o 

c5 

C/3 

X 

1 

60 Deg. 

79* Deg. 

79* Deg. 

I 

79* Deg. 

a J 



















































































































24 TRAVERSE TABLE. 


I Distance. 

«—-- 

11 Deg. 

11} Leg. 

lli Deg. 

11} Deg. 

Distance. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

! 1 

0.98 

0.19 

0.98 

0.20 

0.98 

0.20 

0.98 

0.20 

1 

1 

I 2 

1.96 

0.38 

1.96 

0.39 

1.96 

0.40 

1-96 

0.41 

2 

3 

2.94 

0.57 

2.94 

0.59 

2.94 

0.60 

2.94 

0.61 

3 

4 

3.93 

0.76 

3.92 

0.78 

3.92 

0.80 

3.92 

0.82 

4 

5 

4.91 

0.95 

4.90 

0.98 

4.90 

1.00 

4.90 

1.02 

5 

6 

5.89 

1.14 

5.88 

1.17 

5.88 

1.20 

5.87 

1.22 

6 

7 

6.87 

1.34 

6.87 

1.37 

6.86 

1.40 

6.85 

1.43 

7 

8 

7.85 

1.53 

7.85 

1.56 

7.84 

1.59 

7.83 

1.63 

8 

9 

8.83 

1.72 

8.83 

1.76 

8.82 

1.79 

8.81 

1.83 

9 

10 

9.82 

1.91 

9.81 

1.95 

9.80 

1.99 

9.79 

2.04 

10 

11 

10.80 

2.10 

10.79 

2.15 

10.78 

2.19 

10.77 

2.24 

11 

12 

11.78 

2.29 

11.77 

2.34 

11.76 

2.39 

11.75 

2.44 

12 

13 

12.76 

2.48 

12.75 

2.54 

12.74 

2.59 

12.73 

2.65 

13 

14 

13.74 

2.67 

13.73 

2.73 

13.72 

2.79 

13.71 

2.85 

14 

15 

14.72 

2.86 

14.71 

2.93 

14.70 

2.99 

14.69 

3.06 

15 

16 

15.71 

3.05 

15.69 

3.12 

15.68 

3.19 

15.66 

3.26 

16 

17 

16.69 

3.24 

16.67 

3.32 

16.66 

3.39 

16.64 

3.46 

17 

18 

17.67 

3.43 

17.65 

3.51 

17.64 

3.59 

17.62 

3.66 

18 

19 

18.65 

3.63 

18.63 

3.71 

18.62 

3.79 

18.60 

3.87 

19 

20 

19.63 

3.82 

19.62 

3.90 

19.60 

3.99 

19.58 

4.07 

20 

21 

20.61 

4.01 

20.60 

4.10 

20.58 

4.19 

20.56 

4.28 

21 

22 

21.60 

4.20 

21.58 

4.29 

21.56 

4.39 

21.54 

4.48 

22 

23 

22.58 

4.39 

22.56 

4.49 

22.54 

4.59 

22.52 

4.68 

23 

24 

23.56 

4.58 

23.54 

4.68 

23.52 

4.78 

23.50 

4.89 

24 

25 

24.54 

4.77 

24.52 

4.88 

24.50 

4.98 

24.48 

5.09 

25 

26 

25.52 

4.96 

25.50 

5.07 

25.48 

5.18 

25.46 

5.30 

26 

27 

26.50 

5.15 

26.48 

5.27 

26.46 

5.38 

26.43 

5.50 

27 

28 

27.49 

5.34 

27.46 

5.46 

27.44 

5.58 

27.41 

5.70 

28 

29 

28.47 

5.53 

28.44 

5.66 

28.42 

5.78 

28.39 

5.91 

29 

30 

29.45 

5.72 

29.42 

5.85 

29.40 

5.98 

29.37 

6.11 

30 

31 

30.43 

5.92 

30.40 

6.05 

30.38 

6.18 

30.35 

6.31 

31 

32 

31.41 

6.11 

31.39 

6.24 

31.36 

6.38 

31.33 

6.52 

32 

33 

32.39 

6.30 

32.37 

6.44 

32.34 

6.58 

32.31 

6.72 

33 

34 

33.38 

6.49 

33.35 

6.63 

33.32 

6.78 

33.29 

6.92 

34 

35 

34.36 

6.68 

34.33 

6.83 

34.30 

6.98 

34.27 

7.13 

35 

36 

35.34 

6.87 

35.31 

7.02 

35.28 

7.18 

35.25 

7.33 

36 

37 

36.32 

7.06 

36.29 

7.22 

36.26 

7.38 

36.22 

7.53 

37 

38 

37.30 

7.25 

37.27 

7.41 

37.24 

7.58 

37.20 

7.74 

38 

39 

38.28 

7.44 

38.25 

7.61 

38.22 

7.78 

38.18 

7.94 

39 

40 

39.27 

7.63 

39.23 

* 

7.80 

39.20 

7.97 

39.16 

8.15 

40 

41 

40.25 

7.82 

40.21 

8.00 

40.18 

8.17 

40.14 

8.35 

41 

42 

41.23 

8.01 

41.19 

8.19 

41.16 

8.37 

41.12 

8.55 

42 

43 

42.21 

8.20 

42.17 

8.39 

42.14 

8.57 

42.10 

8.76 

43 

44 

43.19 

8.40 

43.15 

8.58 

43.12 

8.77 

43.08 

8.96 

44 

45 

44.17 

8.59 

44.14 

8.78 

44.10 

8.97 

44.06 

9.16 

45 

46 

45.15 

8.78 

45.12 

8.97 

45.08 

9.17 

45.04 

9.37 

46 

47 

46.14 

8.97 

46.10 

9.17 

46.06 

9.37 

46.02 

9.57 

47 

48 

47.12 

9.16 

47.08 

9.36 

47.04 

9.57 

46.99 

9.78 

48 

49 

48.10 

9.35 

48.06 

9.56 

48.02 

9.77 

47.97 

9.98 

49 

50 

49.08 

9.54 

49.04 

9.75 

49.00 

9.97 

48.95 

10.18 

50 1 

Distance. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

• 

Q> 

O 

g 

-W | 

Ol 

• H 1 

Q ! 

79 Deg. 

* 

78} Deg. 

78} Deg. 

78} Deg. 


4* 































































































TRAVERSE TABLE 


25 


g 

C/3 * 
ft" 

5» 

3 

11 Deg. 

Hi Deg. 

lli Deg. 

Ilf Deg. 

U 

id 

rt- 

o 

o 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

P 

O 

CD 

51 

50.06 

9.73 

50.02 

9.95 

49.98 

10.17 

49.93 

10.39 

51 

5.2 

51.04 

9.92 

51.00 

10.14 

50.96 

10.37 

50.91 

10.59 

52 

53 

52.03 

10.11 

51.98 

10.34 

51.94 

10.57 

51.89 

10.79 

53 

54 

53.01 

10.30 

52.96 

10.53 

52.92 

10.77 

52.87 

11.00 

54 

55 

53.99 

10.49 

53.94 

10.73 

53.90 

10.97 

53.85 

11.20 

55 

56 

54.97 

10.69 

54.92 

10.93 

54.88 

11.16 

54.83 

11.40 

56 

57 

55.95 

10.88 

55.90 

11.12 

55.86 

11.36 

55.81 

11.61 

57 

58 

56.93 

11.07 

56.89 

11.32 

56.84 

11.56 

56.78 

11.81 

58 

59 

57.92 

11.26 

57.87 

11.51 

57.82 

11.76 

57.76 

12.01 

59 

60 

58.90 

11.45 

58.85 

11.71 

58.80 

11.96 

58.74 

12.22 

60 

61 

59.88 

11.64 

59.83 

11.90 

59.78 

12.16 

59.72 

12.42 

61 

62 

60.86 

11.83 

60.81 

12.10 

60.76 

12.36 

60.70 

12.63 

62 

63 

61.84 

12.02 

61.79 

12.29 

61.74 

12.56 

61.68 

12.83 

63 

64 

62.82 

12.21 

62.77 

12.49 

62.72 

12.76 

62.66 

13.03 

64 

65 

63.81 

12.40 

63.75 

12.68 

63.70 

12.96 

63.64 

13.24 

65 

66 

64.79 

12.59 

64.73 

12.88 

64.68 

13.16 

64.62 

13.44 

66 

67 

65.77 

12.78 

65.71 

13.07 

65.66 

13.36 

65.60 

13.64 

67 

68 

66.75 

12.98 

66.69 

13.27 

66.63 

13.56 

66.58 

13.85 

68 

69 

67.73 

13.17 

67.67 

13.46 

67.61 

13.76 

67.55 

14.05 

69 

70 

68.71 

13.36 

68.66 

13.66 

68.59 

13.96 

68.53 

14.25 

70 

71 

69.70 

13.55 

69.64 

13.85 

69.57 

14.16 

69.51 

14.46 

71 

72 

70.68 

13.74 

70.62 

14.05 

70.55 

14.35 

70.49 

14.66 

72 

73 

71.66 

13.93 

71.60 

14.24 

71.53 

14.55 

71.47 

14.87 

73 

74 

72.64 

14.12 

72.58 

14.44 

72.51 

14.75 

72.45 

15.07 

74 

75 

73.62 

14.31 

73.56 

14.63 

73.49 

14.95 

73.43 

15.27 

75 

76 

74.60 

14.50 

74.54 

14.83 

74.47 

15.15 

74.41 

15.48 

76 

77 

75.59 

14.69 

75.52 

15.02 

75.45 

15.35 

75.39 

15.68 

77 

78 

76.57 

14.88 

76.50 

15.22 

76.43 

15.55 

76.37 

15.88 

78 

79 

77.55 

15.07 

77.48 

15.41 

77.41 

15.75 

77.34 

16.09 

79 

80 

78.53 

15.26 

78.46 

15.61 

78.39 

15.95 

78.32 

16.29 

80 

81 

79.51 

15.46 

79.44 

15.80 

79.37 

16.15 

79.30 

16.49 

81 

82 

80.49 

15.65 

80.42 

16.00 

80.35 

16.35 

80.28 

16.70 

82 

83 

81.48 

15.84 

81.41 

16.19 

81.33 

16.55 

81.26 

16.90 

83 

84 

82.46 

16.03 

82.39 

16.39 

82.31 

16.75 

82.24 

17.11 

84 

85 

83.44 

16.22 

83.37 

16.58 

83.29 

16.95 

83.22 

17.31 

85 

86 

84.42 

16.41 

84.35 

16.78 

84.27 

17.15 

84.20 

17.51 

86 

87 

85.40 

16.60 

85.33 

16.97 

85.25 

17.35 

85.18 

17.72 

87 

88 

86.38 

16.79 

86.31 

17.17 

86.23 

17.54 

86.16 

17.92 

88 

89 

87.36 

16.98 

87.29 

17.36 

87.21 

17.74 

87.14 

18.12 

89 

90 

88.35 

17.17 

88.27 

17.56 

88.19 

17.94 

88.11 

18.33 

90 

91 

89.33 

17.36 

89.25 

17.75 

89.17 

18.14 

89.09 

18.53 

91 

92 

90.31 

17.55 

90.23 

17.95 

90.15 

18.34 

90.07 

18.74 

92 

93 

91.29 

17.75 

91.21 

18.14 

91.13 

18.54 

91.05 

18.94 

93 

94 

92.27 

17.94 

92.19 

18.34 

92.11 

18.74 

92.03 

19.14 

94 

95 

93.25 

18.13 

93.17 

18.53 

93.09 

18.94 

93.01 

19.35 

95 

96 

94.24 

18.32 

94.16 

18.73 

94.07 

19.14 

93.99 

19.55 

96 

97 

95.22 

18.51 

95.14 

18.92 

95.05 

19.34 

94.97 

19.75 

97 

98 

96.20 

18.70 

96.12 

19.12 

96.03 

19.54 

95.95 

19.96 

98 

99 

97.18 

18.89 

97.10 

19.31 

97.01 

19.74 

96.93 

20-16 

99 

100 

98.16 

19.03 

98.08 

19.51 

97.99 

19.94 

97.90 

20.36 

100 

6 

o. 

Dep. | 

Lat. 

Dep. 

Lat-. ! 

Dep. ^ 

Lat. 

Dep. 

Lat. 

• 

§ 

C/3 

s 

79 Deg. 

> 

781 Deg. 

---y > 

784 Deg. 

|i 

1 

784 Deg. 

< 1 

ci 

-30 

• H 

£5 


D 





































































































26 


TRAVERSE TABLE 


G 

*-• 

GO 

r+ 

P 

12 Deg. 

12! Deg. 

| 

12* Deg. 

12| Deg. | 

• 

U) 

r*' 

P 

23 

s 

o 

o 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

a 

n> 

• 

1 

0.98 

0.21 

0.98 

0.21 

0.98 

0.22 

0.98 

0.22 

1 1 

2 

1.96 

0.42 

1.95 

0.42 

1.95 

0.43 

1.95 

0.44 

2 

3 

2.93 

0.62 

2.93 

0.64 

2.93 

0.65 

2.93 

0.66 

3 

4 

3.91 

0.83 

3.91 

0.85 

3.91 

0.87 

3.90 

0.88 

4 

5 

4.89 

1.04 

4.89 

1.06 

4.88 

1.08 

4.88 

1.10 

5 

6 

5.87 

1.25 

5.86 

1.27 

5.86 

1.30 

5.85 

1.32 

6 

7 

6.85 

1.46 

6.84 

1.49 

6.83 

1.52 

6.83 

1.54 

7 

8 

7.83 

1.66 

7.82 

1.70 

7.81 

1.73 

7.80 

1.77 

8 

9 

8.80 

1.87 

8.80 

1.91 

8.79 

1.95 

8.78 

1.99 

9 

10 

9.78 

2.08 

9.77 

2.12 

9.76 

2.16 

9.75 

2.21 

10 

11 

10.76 

2.29 

10.75 

2.33 

10.74 

2.38 

10.73 

2.43 

11 

12 

11.74 

2.49 

11.73 

2.55 

11.72 

2.60 

11.70 

2.65 

12 

13 

12.72 

2.70 

12.70 

2.76 

12.69 

2.81 

12.68 

2.87 

13 

14 

13.69 

2.91 

13.68 

2.97 

13.67 

3.03 

13.65 

3.09 

14 

15 

14.67 

3.12 

14.66 

3.18 

14.64 

3.25 

14.63 

3.31 

15 

16 

15.65 

3.33 

15.64 

3.39 

15.62 

3.46 

15.61 

3.53 

16 

17 

16.63 

3.53 

16.61 

3.61 

16.60 

3.68 

16.58 

3.75 

17 

18 

17.61 

3.74 

17.59 

3.82 

17.57 

3.90 

17.56 

3.97 

18 

19 

18.58 

3.95 

18.57 

4.03 

18.55 

4.11 

18.53 

4.19 

19 

20 

19.56 

4.16 

19.54 

4.24 

19.53 

4.33 

19.51 

4.41 

20 

21 

20.54 

4.37 

20.52 

4.46 

20.50 

4.55 

20.48 

4.63 

21 

22 

21.52 

4.57 

21.50 

4.67 

21.48 

4.76 

21.46 

4.86 

22 

23 

22.50 

4.78 

22.48 

4.88 

22.45 

4.98 

22.43 

5.08 

23 

24 

23.48 

4.99 

23.45 

5.09 

23.43 

5.19 

23.41 

5.30 

24 

25 

24.45 

5.20 

24.43 

5.30 

24.41 

5.41 

24.38 

5.52 

25 

26 

25.43 

5.41 

25.41 

5.52 

25.38 

5.63 

25.36 

5.74 

26 

27 

26.41 

5.61 

26.39 

5.73 

26.36 

5.84 

26.33 

5.96 

27 

28 

27.39 

5.82 

27.36 

5.94 

27.34 

6.06 

27.31 

6.18 

28 

29 

28.37 

6.03 

28.34 

6.15 

28.31 

6.28 

28.28 

6.40 

29 

30 

29.34 

6.24 

29.32 

6.37 

29.29 

6.49 

29.26 

6.62 

30 

31 

30.32 

6.45 

30.29 

6.58" 

30.27 

6.71 

30.24 

6.84 

31 

32 

31.30 

6.65 

31.27 

6.79 

31.24 

6.93 

31.21 

7.06 

32 

33 

32.28 

6.86 

32.25 

7.00 

32.22 

7.14 

32.19 

7.28 

33 

34 

33.26 

7.07 

33.23 

7.21 

33.19 

7.36 

33.16 

7.50 

34 

35 

34.24 

7.28 

34.20 

7.43 

34.17 

7.58 

34.14 

7.72 

35 

36 

35.21 

7.48 

35.18 

7.64 

35.15 

7.79 

35.11 

7.95 

36 

37 

36.19 

7.69 

36.16 

7.85 

36.12 

8.01 

36.09 

8.17 

37 

38 

37.17 

7.90 

37.13 

8.06 

37.10 

8.22 

37.06 

8.39 

38 

39 

38.15 

8.11 

38.11 

8.27 

38.08 

8.44 

38.04 

8.61 

39 

40 

39.13 

8.32 

39.09 

8.49 

39.05 

8.66 

39.01 

8.83 

40 

41 

40.10 

8.52 

40.07 

8.70 

40.03 

8.87 

39.99 

9.05 

41 

42 

41.08 

8.73 

41.04 

8.91 

41.00 

9.09 

40.96 

9.27 

42 

43 

42.06 

8.94 

42.02 

9.12 

41.98 

9.31 

41.94 

9.49 

43 

44 

43.04 

9.15 

43.00 

9.34 

42.96 

9.52 

42.92 

9.71 

44 

45 

44.02 

9.36 

43.98 

9.55 

43.93 

9.74 

43.89 

9.93 

45 

46 

44.99 

9.56 

44.95 

9.76 

44.91 

9.96 

44.87 

10.15 

46 

47 

45.97 

9.77 

45.93 

9.97 

45.89 

10.17 

45.84 

10.37 

47 

' 48 

46.95 

9.98 

46.91 

10.18 

46.86 

10.39 

46.82 

10.59 

48 

49 

47.93 

10.19 

47.88 

10.40 

47.84 

10.61 

47.79 

10.81 

49 

50 

48.91 

10.40 

48.86 

10.61 

48.81 

10.82 

48.77 

11.03 

50 

V 

o 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

• 

4) 

O 

+-> 

CO 

A 

78 Deg. 

f 

77f Deg. 

77* Deg. 

77* Deg. 

i 

n 

CT5 

*-» 

CO 

Q 


V 



























































































TRAVERSE TABLE 


27 


0 
** • 

CO 

r+- 

P 

a 

12 Deg. 

12£ 

Deg. 

12i 

Deg. 

12f 

Deg. 

d 
>— • 

CO 

P 

o 

(D 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

3 

O 

CD 

• 

51 

49.89 

10.60 

49.84 

10.82 

49.79 

11.04 

49.74 

11.26 

51 

52 

50.86 

10.81 

50.82 

11.03 

50.77 

11.25 

50.72 

11.48 

52 

53 

51.84 

11.02 

51.79 

11.25 

51.74 

11.47 

51.69 

11.70 

53 

54 

52.82 

11.23 

52.77 

11.46 

52.72 

11.69 

52.67 

11.92 

54 

55 

53.80 

11.44 

53.75 

11.67 

53.70 

11.90 

53.64 

12.14 

55 

56 

54.78 

11.64 

54.72 

11.88 

54.67 

12.12 

54.62 

12.36 

56 

57 

55.75 

11.85 

55.70 

12.09 

55.65 

12.34 

55.59 

12.58 

57 

58 

56.73 

12.06 

56.68 

12.31 

56.63 

12.55 

56.57 

12.80 

58 

59 

57.71 

12.27 

57.66 

12.52 

57.60 

12.77 

57.55 

13.02 

59 

60 

58.69 

12.47 

58.63 

12.73 

58.58 

12.99 

58". 52 

13.24 

60 

61 

59.67 

12.68 

59.61 

12.94 

59.55 

13.20 

59.50 

13.46 

61 

62 

60.65 

12.89 

60.59 

13.16 

60.53 

13.42 

60.47 

13.68 

62 

63 

61.62 

13.10 

61.57 

13.37 

61.51 

13.64 

61.45 

13.90 

63 

64 

62.60 

13.31 

62.54 

13.58 

62.48 

13.85 

62.42 

14.12 

64 , 

65 

63.58 

13.51 

63.52 

13.79 

63.46 

14.07 

63.40 

14.35 

65 

66 

64.56 

13.72 

64.50 

14.00 

64.44 

14.29 

64.37 

- 14.57 

66 

67 

65.54 

13.93 

65.47 

14.22 

65.41 

14.50 

65.35 

14.79 

67 

68 

66.51 

14.14 

66.45 

14.43 

66.39 

14.72 

66.32 

15.01 

68 

69 

'67.49 

14.35 

67.43 

14.64 

67.36 

14.93 

67.30 

15.23 

69 

70 

68.47 

14.55 

68.41 

14.85 

68.34 

15.15 

68.27 

15.45 

70 

71 

69.45 

14.76 

69.38 

15.06 

69.32 

15.37 

69.25 

15.67 

71 

72 

70.43 

14.97 

70.36 

15.28 

70.29 

15.58 

70.22 

15.89 

72 

73 

71.40 

15.18 

71.34 

15.49 

71.27 

15.80 

71.20 

16.11 

73 

74 

72.38 

15.39 

72.32 

15.70 

72.25 

16.02 

72.18 

16.33 

74 

75 

73.36 

15.59 

73.29 

15.91 

73.22 

16.23 

73.15 

16.55 

75 

76 

74.34 

15.80 

74.27 

16.13 

74.20 

16.45 

74.13 

16.77 

76 

77 

75.32 

16.01 

75.25 

16.34 

75.17 

16.67 

75.10 

16.99 

77 

78 

76.30 

16.22 

76.22 

16.55 

76.15 

16.88 

76.08 

17.21 

78 

79 

77.27 

16.43 

77.20 

16.76 

77.13 

17.10 

77.05 

17.44 

79 

80 

78.25 

16.63 

78.18 

16.97 

78.10 

17.32 

78.03 

17.66 

80 

81 

79.23 

16.84 

79.16 

17.19 

79.08 

17.53 

79.00 

17.88 

81 

82 

80.21 

17.05 

80.13 

17.40 

80.06 

17.75 

79.98 

18.10 

82 

83 

81.19 

17.26 

81.11 

17.61 

81.03 

17.96 

80.95 

18.32 

83 

84 

82.16 

17.46 

82.09 

17.82 

82.01 

18.18 

81.93 

18.54 

84 

85 

83.14 

17.67 

83.06 

18.04 

82.99 

18.40 

82.90 

18.76 

85 

86 

84.12 

17.88 

84.04 

18.25 

83.96 

18.61 

83.88 

18.98 

86 

87 

85.10 

18.09 

85.02 

18.46 

84.94 

18.83 

84.85 

19.20 

87 

88 

86.08 

18.30 

86.00 

18.67 

85.91 

19.05 

85.83 

19.42 

88 

89 

87.06 

18.50 

86.97 

18.88 

86.89 

19.26 

86.81 

19.64 

89 

90 

88.03 

18.71 

87.95 

19.10 

87.87 

19.48 

87.78 

19.86 

90 | 

91 

89.01 

18.92 

88.93 

19.31 

88.84 

19.70 

88.76 

20.08 

91 

92 

89.99 

19.13 

89.91 

19.52 

89.82 

19.91 

89.73 

20.30 

92 J 

93 

90.97 

19.34 

90.88 

19.73 

90.80 

20.13 

90.71 

20.52 

93 1 

94 

91.95 

19.54 

91.86 

19.94 

91.77 

20.35 

91.68 

'20.75 

94 I 

95 

92.92 

19.75 

92.84 

20.16 

92.75 

20.56 

92.66 

20.97 

95 | 

96 

93.90 

19.96 

93.81 

20.37 

93.72 

20.78 

93.63 

21.19 

96 

97 

94.88 

20.17 

94.79 

20.58 

94.70 

20.99 

94.61 

21.41 

97 

98 

95.86 

20.38 

95.77 

20.79 

95.68 

21.21 

95.58 

21.63 

98 

99 

96.84 

20.58 

96.75 

21.01 

96.65 

21.43 

96.56 

21.85 

99 

100 

97.81 

20.79 

97.72 

21.22 

97.63 

21.64 

97.53 

22.07 

100 

«; 

o 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

<J 

o 

G 

d 

+-> 

• M 

Q 

78 Deg. 

77| Deg. 

$ 

77£ Deg. 

77i Deg. 

d 
■*-> 
c n 

P 





























































































28 


TRAVERSE TABLE. 


Di !Zl 

13 Deg. 

13^ Deg. 

13* Deg. 

13| Deg. 

Distance. 

Lat. 

Dep. 

- Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

1 

0.97 

0.23 

0.97 

0.23 

0.97 

0.23 

0.97 

0.24 

1 

2 

1.95 

0.45 

1.95 

0.46 

1.95 

0.47 

1.94 

0.48 

2 

3 

2.92 

0.67 

2.92 

0.69 

2.92 

0.70 

2.91 

0.71 

3 

4 

3.90 

0.90 

3.89 

0.92 

3.89 

0.93 

3.89 

0.95 

4 

5 

4.87 

1.12 

4.87 

1.15 

4.86 

1.17 

4.86 

1.19 

5 

6 

5.85 

1.35 

5.84 

1.38 

5.83 

1.40 

5.83 

1.43 

6 

7 

6.82 

1.57 

6.81 

1.60 

6.81 

1.63 

6.80 

1.66 

7 

8 

7.80 

1.80 

7.79 

1.83 

7.78 

1.87 

7.77 

1.90 

8 

9 

8.77 

2.02 

8.76 

2.06 

8.75 

2.10 

8.74 

2.14 

9 

10 

9.74 

2.25 

9.73 

2.29 

9.72 

2.33 

9.71 

2.38 

10 

11 

10.72 

2.47 

10.71 

2.52 

10.70 

2.57 

10.68 

2.61 

11 

12 

11.69 

2.70 

11.68 

2.75 

11.67 

2.80 

11.66 

2.85 

12 

13 

12.67 

2.92 

12.65 

2.98 

12.64 

3.03 

12.63 

3.09 

13 

14 

13.64 

3.15 

13.63 

3.21 

13.61 

3.27 

13.60 

3.33 

14 

15 

14.62 

3.37 

14.60 

3.44 

14.59 

3.50 

14.57 

3.57 

15 

16 

15.59 

3.60 

15.57 

3.67 

15.56 

3.74 

15.54 

3.80 

16 

17 

16.57 

3.82 

16.55 

3.90 

16.53 

3.97 

16.51 

4.04 

17 

18 

17.54 

4.05 

17.52 

4.13 

17.50 

4.20 

17.48 

4.28 

18 

19 

18.51 

4.27 

18.49 

4.35 

18.48 

4.44 

18.46 

4.52 

19 

20 

19.49 

4.50 

19.47 

4.58 

19.45 

4.67 

19.43 

4.75 

20 

21 

20.46 

4.72 

20.44 

4.81 

20.42 

4.90 

20.40 

4.99 

21 

22 

21.44 

4.95 

21.41 

5.04 

21.39 

5.14 

21.37 

5.23 

22 

23 

22.41 

5.17 

22.39 

5.27 

22.36 

5.37 

22.34 

5.47 

23 

24 

23.38 

5.40 

23.36 

5.50 

23.34 

5.60 

23.31 

5.70 

24 

25 

24.36 

5.62 

24.33 

5.73 

24.31 

5.84 

24.28 

5.94 

25 

26 

25.33 

5.85 

25.31 

5.96 

25.28 

6.07 

25.25 

6.18 

26 

27 

26.31 

6.07 

26.28 

6.19 

26.25 

6.30 

26.23 

6.42 

27 

28 

27.28 

6.30 

27.25 

6.42 

27.23 

6.54 

27.20 

6.66 

28 

29 

28.26 

6.52 

28.23 

6.65 

28.20 

6.77 

28.17 

6.89 

29 

30 

29.23 

6.75 

29.20 

6.88 

29.17 

7.00 

29.14 

7.13 

30 

31 

30.21 

6.97 

30.17 

7.11 

30.14 

7.24 

30.11 

7.37 

31 

32 

31.18 

7.20 

31.15 

7.33 

31.12 

7.47 

31.08 

7.61 

32 

33 

32i 15 

7.42 

32.12 

7.56 

32.09 

7.70 

32.05 

7.84 

33 

34 

33.13 

7.65 

33.09 

7.79 

33.06 

7.94 

33.03 

8.08 

34 

35 

34.10 

7.87 

34.07 

8.02 

34.03 

8.17 

34.00 

8.32 

35 

36 

35.08 

8.10 

35.04 

8.25 

35.01 

8.40 

34.97 

8.56 

36 

37 

36.05 

8.32 

36.02 

8.48 

35.98 

8.64 

35.94 

8.79 

*37 

38 

37.03 

8.55 

36.99 

8.71 

36.95 

8.87 

36.91 

9.03 

38 

39 

38.00 

8.77 

37.96 

8.94 

37.92 

9.10 

37.88 

9.27 

39 

40 

38.97 

9.00 

38.94 

9.17 

38.89 

9.34 

38.85 

9.51 

40 

41 

39.95 

9.22 

39.91 

9.40 

39.87 

9.57 

39.83 

9.75 

41 

42 

40.92 

9.45 

40.88 

9.63 

40.84 

9.80 

40.80 

9.98 

42 

43 

41.90 

9.67 

41.86 

9.86 

41.81 

10.04 

41.77 

10.22 

43 

44 

42.87 

9.90 

42.83 

10.08 

42.78 

10.27 

42.74 

10.46 

44 

45 

43.85 

10.12 

43.80 

10.31 

43.76 

10.51 

43.71 

10.70 

45 

46 

44.82 

10.35 

44.78 

10.54 

44.73 

10.74 

44.68 

10.93 

46 

47 

45.80 

10.57 

45.75 

10.77 

45.70 

10.97 

45.65 

11.17 

47 

48 

46.77 

10-80 

46.72 

11.00 

46.67 

11.21 ! 

46.62 

11.41 

48 

49 

47.74 

11.02 

47.70 

11.23 

47.65 

11.44 

47.60 

11.65 

49 

50 

48.72 

11.25 

48.67 

11.46 

48.62 

11.67 

48.57 

11.88 

50 

Distance. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

|j Distance. 

77 Deg. 

* u 

76| Deg. 

76* Deg. 

76* Deg. 






























































































TRAVERSE TABLE, 


29 


G 

b-> • 

TO 
ct- 

p 

0 

o 

rt> 

• 

13 Deg. 

; 

134 Deg. 

134 Deg. 

13| Deg. 

o 
>—< . 
it, 

r 4 * 

P 

Lat. 

Dep. 

Lat. 

Dep. 

Lat, 

Dep. 

Lat. 

Dep. 

p 

o 

a 

51 

49.69 

11.47 

49.64 

11.69 

49.59' 

11.91 

49.54 

12.12 

51 

52 

50.67 

11.70 

50.62 

11.92 

50.56 

12.14 

50.51 

12.36 

52 

53 

51.64 

11.92 

51.59 

12.15 

51.54 

12.37 

51.48 

12.60 

53 

54 

52.62 

12.15 

52.56 

12.38 

52.51 

12.61 

52.45 

12.84 

54 

55 

53.59 

12.37 

53.54 

12.61 

53.48 

12.84 

53.42 

13.07 

55 

56 

54.56 

12.60 

54.51 

12.84 

54.45 

13.07 

54.40 

13.31 

56 

57 

55.54 

12.82 

55.48 

13.06 

55.43 

13.31 

55.37 

13.55 

57 

58 

56.51 

13.05 

56.46 

13.29 

56.40 

13.54 

56.34 

13.79 

58 

59 

57.49 

13.27 

57.43 

13.52 

57.37 

13.77 

57.31 

14.02 

59 

60 

58.46 

13.50 

58.40 

13.75 

58.34 

14.01 

58.28 

14.26 

60 

61 

59.44 

13.72 

59.38 

13.98 

59.31 

14.24 

59.25 

14.50 

61 

62 

60.41 

13.95 

60.35 

14.21 

60.29 

14.47 

60.22 

14.74 

62 

63 

61.39 

14.17 

61.32 

14.44 

61.26 

14.71 

61.19 

14.97 

63 

64 

62.36 

14.40 

62.30 

14.67 

62.23 

14.94 

62.17 

15.21 

64 

65 

63.33 

14.62 

63.27 

14.90 

63.20 

15.17 

63.14 

15.45 

65 

66 

64.31 

14.85 

64.24 

15.13 

64.18 

15.41 

64.11 

15.69 

66 

67 

65.28 

15.07 

65.22 

15.36 

65.15 

15.64 

65.08 

15.93 

67 

68 

66.26 

15.30 

66.19 

15.59 

66.12 

15.87 

66.05 

16.16 

68 

69 

67.23 

15.52 

67.16 

15.81 

67.09 

16.11 

67.02 

16.40 

69 

70 

68.21 

15.75 

68.14 

16.04 

68.07 

16.34 

67.99 

16.64 

70 

71 

69.18 

15.97 

69.11 

16.27 

69.04 

16.57 

68.97 

16.88 

71 

72 

70.15 

16.20 

70.08 

16.50 

70.01 

16.81 

69.94 

17.11 

72 

73 

71.13 

16.42 

71.06 

16.73 

70.98 

17.04 

70.91 

17.35 

73 

74 

72.10 

16.65 

72.03 

16.96 

71.96 

17.28 

71.88 

17.59 

74 

75 

73.08 

16.87 

73.00 

17.19 

72.93 

17.50 

72.85 

17.83 

75 

76 

74.05 

17.10 

73.98 

17.42 

73.90 

17.74 

73.82 

18.06 

76 

77 

75.03 

17.32 

74.95 

17.65 

74.87 

17.98 

74.79 

18.30 

77 

78 

76.00 

17.55 

75.92 

17.88 

75.84 

18.21 

75.76 

18.54 

78 

79 

76.98 

17.77 

76.90 

18.11 

76.82 

18.44 

76.74 

18.78 

79 

80 

77.95 

18.00 

77.87 

18.34 

77.79 

18.68 

77.71 

19.01 

80 

81 

78.92 

18.22 

78.84 

18.57 

78.76 

18.91 

78.68 

19.25 

81 

82 

79.90 

18.45 

79.82 

18.79 

79.73 

19.14 

79.65 

19.49 

82 

83 

80.87 

18.67 

80.79 

19.02 

80.71 

19.38 

80.62 

19.73 

83 

84 

81.85 

18.90 

81.76 

19.25 

81.68 

19.61 

81.59 

19.97 

84 

85 

82.82 

19.12 

82.74 

19.48 

82.65 

19.84 

82.56 

20.20 

85 

86 

83.80 

19.35 

83.71 

19.71 

83.62 

20.08 

83.54 

20.44 

86 

87 

84.77 

19.57 

84.68 

19.94 

84.60 

20.31 

84.51 

20.68 

87 

88 

85.74 

19.80 

85.66 

20.17 

85.57 

20.54 

85.48 

20.92 

88 

89 

86.72 

20.02 

86.63 

20.40 

86.54 

20.78 

86.45 

21.15 

89 

90 

87.69 

20.25 

87.60 

20.63 

87.51 

21.01 

87.42 

21.39 

90 

91 

88.67 

20.47 

88.58 

20.86 

88.49 

21.24 

88.39 

21.63 

91 

92 

89.64 

20.70 

89.55 

21.09 

89.46 

21.48 

89.36 

21.87 

92 

93 

90.62 

20.92 

90.52 

21.32 

90.43 

21.71 

90.33 

22.10 

93 

94 

91.59 

21.15 

91.50 

21.54 

91.40 

21.94 

91.31 

22.34 

94 

95 

92.57 

21.37 

92.47 

21.77 

92.38 

22.18 

92.28 

22.58 

95 

96 

93.54 

21.60 

93.44 

22.00 

93.35 

22.41 

93.25 

22.82 

96 

97 

94.51 

21.82 

94.42 

22.23 

94.32 

22.64 

94.22 

23.06 

97 

98 

95.49 

22.05 

95.39 

22.46 

95.29 

22.88 

95.19 

23.29 

98 

99 

96.46 

22.27 

96.36 

22.69 

96.26 

23.11 

96.16 

23.53 

99 

100 

97.44 

22.50 

97.34 

22.92 

97.24 

23.34 

97.13 

23.77 

100 

6 

G 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 1 

Lat. 

Dep. 

Lat. 

G 

O 

£3 

c 

d 

-4-> 

p 

77 Deg. 

76| Deg. 

764 Deg. 

76! Deg. 

d 

C/3 

• H 

P 




















































































30 


TRAVERSE TABLE. 


d 
►— • 

r+ 

v> 

14 Deg. 

14i Deg. 

14$ Deg. 

14f Deg. 

d 
*-* • 

C/5 

v> 

13 

a 

o 

• 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

a 

m 

• 

1 

0.97 

0.24 

0.97 

0.25 

0.97 

0.25 

0.97 

0.25 

1 

2 

1.94 

0.48 

1.94 

0.49 

1.94 

0.50 

1.93 

0.51 

2 

3 

2.91 

0.73 

2.91 

0.74 

2.90 

0.75 

2.90 

0.76 

3 

4 

3.88 

0.97 

3.88 

0.98 

3.87 

1.00 

3.87 

1.02 

4 

5 

4.85 

1.21 

4.85 

1.23 

4.84 

1.25 

4.84 

1.27 

5 

6 

5.82 

1.45 

5.82 

1.48 

5.81 

1.50 

5.80 

1.53 

6 

7 

6.79 

1.69 

6.78 

1.72 

6.78 

1.75 

6.77 

1.78 

7 

8 

7.76 

1.94 

7.75 

1.97 

7.75 

2.00 

7.74 

2.04 

8 

9 

8.73 

2.18 

8.72 

2.22 

8.71 

2.25 

8.70 

2.29 

9 

10 

9.70 

2.42 

9.69 

2.46 

9.68 

2.50 

9.67 

2.55 

10 

11- 

10.67 

2.66 

10.66 

2.71 

10.65 

2.75 

10.64 

2.80 

11 

12 

11.64 

2.90 

11.63 

2.95 

11.62 

3.00 

11.60 

3.06 

12 

13 

12.61 

3.15 

12.60 

3.20 

12.59 

3.25 

12.57 

3.31 

13 

14 

13.58 

3.39 

13.57 

3.45 

13.55 

3.51 

13.54 

3.56 

14 

15 

14.55 

3.63 

14.54 

3.69 

14.52 

3.76 

14.51 

3.82 

15 

16 

15.52 

3.87 

15.51 

3.94 

15.49 

4.01 

15.47 

4.07 

16 

17 

16.50 

4.11 

16.48 

4.18 

16.46 

4.26 

16.44 

4.33 

17 

18 

17.47 

4.35 

17.45 

4.43 

17.43 

4.51 

17.41 

4.58 

18 

19 

18.44 

4.60 

18.42 

4.68 

18.39 

4.76 

18.37 

4.84 

19 

20 

19.41 

4.84 

19.38 

4.92 

19.36 

5.01 

19.34 

5.09 

20 

21 

20.38 

5.08 

20.35 

5.17 

20.33 

5.26 

20.31 

5.35 

21 

22 

21.35 

5.32 

21.32 

5.42 

21.30 

5.51 

21.28 

5.60 

22 

23 

22.32 

5.56 

22.29 

5.66 

22.27 

5.76 

22.24 

5.86 

23 

24 

23.29 

5.81 

23.26 

5.91 

23.24 

6.01 

23.21 

6.11 

24 

25 

24.26 

6.05 

24.23 

6.15 

24.20 

6.26 

24.18 

6.37 

25 

26 

25.23 

6.29 

25.20 

6.40 

25.17 

6.51 

25.14 

6.62 

26 

27 

26.20 

6.53 

26.17 

6.65 

26.14 

6.76 

26.11 

6.87 

27 

28 

27.17 

6.77 

27.14 

6.89 

27.11 

7.01 

27.08 

7.13 

28 

29 

28.14 

7.02 

28.11 

7.14 

28.08 

7.26 

28.04 

7.38 

29 

30 

29.11 

7.26 

29.08 

7.38 

29.04 

7.51 

29.01 

7.64 

30 

31 

30.08 

7.50 

30.05 

7.63 

30.01 

7.76 

29.98 

7.89 

31 

32 

31.05 

7.74 

31.02 

7.88 

30.98 

8.01 

30.95 

8.15 

32 

33 

32.02 

7.98 

31.98 

8.12 

31.95 

8.26 

31.91 

8.40 

33 

34 

32.99 

8.23 

32.95 

8.37 

32.92 

8.51 

32.88 

8.66 

34 

35 

33.96 

8.47 

33.92 

8.62 

33.89 

8.76 

33.85 

8.91 

35 

36 

34.93 

8.71 

34.89 

8.86 

34.85 

9.01 

34.81 

9.17 

36 

37 

35.90 

8.95 

35.86 

9.11 

35.82 

9.26 

35.78 

9.42 

37 

38 

36.87 

9.19 

36.83 

9.35 

36.79 

9.51 

36.75 

9.67 

38 

39 

37.84 

9.44 

37.80 

9.60 

37.76 

9.76 

37.71 

9.97 

39 

40 

38.81 

9.68 

38.77 

9.85 

38.73 

10.02 

38.68 

10.18 

40 

41 

39.78 

9.92 

39.74 

10.09 

39.69 

10.27 

39.65 

10.44 

41 

42 

40.75 

10.16 

40.71 

10.34 

40.66 

10.52 

40.62 

10.69 

42 

43 

41.72 

10.40 

41.68 

10.58 

41.63 

10.77 

41.58 

10.95 

43 

44 

42.69 

10.64 

42.65 

10.83 

42.60 

11.02 

42.55 

11.20 

44 

45 

43.66 

10.89 

43.62 

11.08 

43.57 

11.27 

43.52 

11.46 

45 

46 

44.63 

11.13 

44.58 

11.32 

44.53 

11.52 

44.48 

11.71 

46 

47 

45.60 

11.37 

45.55 

11.57 

45.50 

11.77 

45.45 

11.97 

47 

48 

46.57 

11.61 

46.52 

11.82 

46.47 

12.02 

46.42 

12.22 

48 

49 

47.54 

11.85 

47.49 

12.06 

47.44 

12.27 

47.39 

12.48 

49 

50 

48.51 

12.10 

48.46 

12.31 

48.41 

12.52 

48.35 

12.73 

50 

© 

© 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

© 

o 

a 

m 

s 

76 Deg. 

75| Deg. 

75£ Deg. 1 

75i Deg. 

£ 

d 

tn 

5 























































































TRAVERSE TABLE 


31 


o 
»— • 

CO 

(-*- 

p 

a 

14 Deg. 

14* 

Deg. 

14* 

Deg. 

14} 

Deg. 

& 

*—•. 

tn 

r** 

p 

o 

ct> 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

s 

o 

? 

51 

49.49 

12.34 

49.43 

12.55 

49.38 

12.77 

49.32 

12.98 

51 

52 

50.46 

12.58 

50.40 

12.80 

50.34 

13.02 

50.29 

13.24 

52 

53 

51.43 

12.82 

51.37 

13.05 

51.31 

13.27 

51.25 

13.49 

53 

54 

52-40 

13.06 

52.34 

13.29 

52.28 

13.52 

52.22 

13.75 

54 

55 

53.37 

13.31 

53.31 

13.54 

53.25 

13.77 

53.19 

14.00 

55 

56 

54.34 

13.55 

54.28 

13.78 

54.22 

14.02 

54.15 

14.26 

56 

57 

55.31 

13.79 

55.25 

14.03 

55.18 

14.27 

55.12 

14.51 

57 

58 

56.28 

14.03 

56.22 

14.28 

56.15 

14.52 

56.09 

14.77 

58 

59 

57.25 

14.27 

57.18 

14.52 

57.12 

14.77 

57.06 

15.02 

59 

60 

58.22 

14.52 

58.15 

14.77 

58.09 

15.02 

58.02 

15.28 

60 

61 

59.19 

14.76 

59.12 

15.02 

59.06 

15.27 

58.99 

15.53 

61 

62 

60.16 

15.00 

60.09 

15.26 

60.03 

15.52 

59.96 

15.79 

62 

63 

61.13 

15.24 

61.06 

15.51 

60.99 

15.77 

60.92 

16.04 

63 

64 

62.10 

15.48 

62.03 

15.75 

61.96 

16.02 

61.89 

16.29 

64 

65 

63.07 

15.72 

63.00 

16.00 

62.93 

16.27 

62.86 

16.55 

65 

66 

64.04 

15.97 

63.97 

16.25 

63.90 

16.53 

63.83 

16.80 

66 

67 

65.01 

16.21 

64.94 

16.49 

64.87 

16.78 

64.79 

17.06 

67 

68 

65.98 

16.45 

65.91 

16.74 

65.83 

17.03 

65.76 

17.31 

68 

69 

66.95 

16.69 

66.88 

16.98 

66.80 

17.28 

66.73 

17.57 

69 

70 

67.92 

16.93 

67.85 

17.23 

67.77 

17.53 

67.69 

17.82 

70 

71 

68.89 

17.18 

68.82 

17.48 

68.74 

17.78 

68.66 

18.08 

71 

72 

69.86 

17.42 

69.78 

17.72 

69.71 

18.03 

69.63 

18.33 

72 

73 

70.83 

17.66 

70.75 

17.97 

70.67 

18.28 

70.59 

18.59 

73 

74 

71.80 

17.90 

71.72 

18.22 

71.64 

18.53 

71.56 

18.84 

74 

75 

72.77 

18.14 

72.69 

18.46 

72.61 

18.78 

72.53 

19.10 

75 

76 

73.74 

18.39 

73.66 

18.71 

73.58 

19.03 

73.50 

19.35 

76 

77 

74.71 

18.63 

74.63 

18.95 

74.55 

19.28 

74.46 

19.60 

77 

78 

75.68 

18.87 

75.60 

19.20 

75.52 

19.53 

75.43 

19.86 

78 

79 

76.65 

19.11 

76.57 

19.45 

76.48 

19.78 

76.40 

20.11 

79 

80 

77.62 

19.35 

77.54 

19.69 

77.45 

20.03 

77.36 

20.37 

80 

81 

78.59 

19.60 

78.51 

19.94 

78.42 

20.28 

78.33 

20.62 

81 

82 

79.56 

19.84 

79.48 

20.18 

79.39 

20.53 

79.30 

20.88 

82 

83 

80.53 

20.08 

80.45 

20.43 

80.36 

20.78 

80.26 

21.13 

83 

84 

81.50 

20.32 

81.42 

20.68 

81.32 

21.03 

81.23 

21.39 

84 

85 

82.48 

20.56 

82.38 

20.92 

82.29 

21.28 

82.20 

21.64 

85 

86 

83.45 

20.81 

83.35 

21.17 

83.26 

21.53 

83.17 

21.90 

86 

87 

84.42 

21.05 

84.32 

21.42 

84.23 

21.78 

84.13 

22.15 

87 

88 

85.39 

21.29 

85.29 

21.66 

85.20 

22.03 

85.10 

22.41 

88 

89 

86.36 

21.53 

86.26 

21.91 

86.17 

22.28 

86.07 

22.66 

89 

90 

87.33 

21.77 

87.23 

22.15 

87.13 

22.53 

87.03 

22.91 

90 

j 91 

88.30 

22.01 

88.20 

22.40 

88.10 

22.78 

88.00 

23.17 

91 

92 

89.27 

22.26 

89.17 

22.65 

89.07 

23.04 

88.97 

23.42 

92 

93 

90.24 

22.50 

90.14 

22.89 

90.04 

23.29 

89.94 

23.68 

93 

94 

91.21 

22.74 

91.11 

23.14 

91.01 

23.54 

90.90 

23.93 

94 

95 

92.18 

22.98 

92.08 

23.38 

91.97 

23.79 

91.87 

24.19 

95 

96 

93.15 

23.22 

93.05 

23.63 

92.94 

24.04 

92.84 

■24.44 

96 

97 

94.12 

23.47 

94.02 

23.88 

93.91 

24.29 

93.80 

24.70 

97 

98 

95.09 

23.71 

94.98 

24.12 

94.88 

24.54 

94.77 

24.95 

98 

99 

96.06 

23.95 

95.95 

24.37 

95.85 

24.79 

95.74 

25.21 

99 

100 

97.03 

24.19 

96.92 

24.62 

96.81 

25.04 

96.70 

25.46 

100 

ol 

o 

Dep. 1 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

G> 

o 

P 

d 

•w 

rn 

• H 

Q 

76 Deg. 

75| Deg. 

75* Deg. 

75* Deg. 

a 
—> 

CO 

Q 





















































































32 


TRAVERSE TABLE 


d 

t—- • 

(12 

rt* 

» 

0 

o 

<T> 

15 Deg. 

15} Deg. 

15} Deg. | 

15} Deg. 

Distance. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

1 

0.97 

0.26 

0.96 

0.26 

0.96 

0.27 

0.96 

0.27 

1 

2 

1.93' 

0.52 

1.93 

0.53 

1.93 

0.53 

1.92 

0.54 

2 

3 

2.90 

0.78 

2.89 

0.79 

2.89 

0.80 

2.89 

0.81 

3 

4 

3.86 

1.04 

3.86 

1.05 

3.85 

1.07 

3.85 

1.09 

4 

5 

4.83 

1.29 

4.82 

1.32 

4.82 

1.34 

4.81 

1.36 

5 

6 

5.80 

1.55 

5.79 

1.58 

5.78 

1.60 

5.77 

1.63 

6 

j 7 

6.76 

1.81 

6.75 

1.84 

6.75 

1.87 

6.74 

1.90 

7 

3 

7.73 

2.07 

7.72 

2.10 

7.71 

2.14 

7.70 

2.17 

8 

9 

8.69 

2.33 

8.68 

2.37 

8.67 

2.41 

8.66 

2.44 

9 

10 

9.66 

2.59 

9.65 

2.63 

9.64 

2.67 

9.62 

2.71 

10 

ii 

10.63 

2.85 

10.61 

2.89 

10.60 

2.94 

10.59 

2.99 

ii : 

12 

11.59 

3.11 

11.58 

3.16 

11T56 

3.21 

11.55 

3.26 

12 

13 

12.56 

3.36 

12.54 

3.42 

12.53 

3.47 

12.51 

3.53 

13 

14 

13.52 

3.62 

13.51 

3.68 

13.49 

3.74 

13.47 

3.80 

14 

15 

14.49 

3.88 

14.47 

3.95 

14.45 

4.01 

14.44 

4.07 

15 

16 

15.45 

4.14 

15.44 

4.21 

15.42 

4.28 

15.40 

4.34 

16 

17 

16.42 

4.40 

16.40 

4.47 

16.38 

4.54 

16.36 

4.61 

17 

18 

17.39 

4.66 

17.37 

4.73 

17.35 

4.81 

17.32 

4.89 

18 

19 

18.35 

4.92 

18.33 

5.00 

18.31 

5.08 

18.29 

5.16 

19 

20 

19.32 

5.18 

19.30 

5.26 

19.27 

5.34 

19.25 

5.43 

20 

21 

20.23 

5.44 

20.26 

5.52 

20.24 

5.61 

20.21 

5.70 

21 

22 

21.25 

5.69 

21.23 

5.79 

21.20 

5.88 

21.17 

5.97 

22 

23 

22.22 

5.95 

22.19 

6.05 

22.16 

6.15 

22.14 

6.24 

23 

24 

23.18 

6.21 

23.15 

6.31 

23.13 

6.41 

23.10 

6.51 

24 

25 

24.15 

6.47 

24.12 

6.58 

24.09 

6.68 

24.06 

6.79 

25 

26 

25.11 

6.73 

25.08 

6.84 

25.05 

6.95 

25.02 

7.06 

26 

27 

26.03 

6.99 

26.05 

7.10 

26.02 

7.22 

25.99 

7.33 

27 

28 

27.05 

7.25 

27.01 

7.36 

26.98 

7.48 

26.95 

7.60 

28 

29 

28.01 

7.51 

27.98 

7.63 

27.95 

7.75 

27.91 

7.87 

29 

30 

28.98 

7.76 

28.94 

7.89 

28.91 

8.02 

28.87 

8.14 

30 

31 

29.94 

8.02 

29.91 

8.15 

29.87 

8.28 

29.84 

8.41 

31 

32 

30.91 

8.28 

30.87 

8.42 

30.84 

8.55 

30.80 

8.69 

32 

33 

31.88 

8.54 

31.84 

8.68 

31.80 

8.82 

31.76 

8.96 

33 

34 

32.84 

8.80 

32.80 

8.94 

32.76 

9.09 

32.72 

9.23 

34 

35 

33.81 

9.06 

33.77 

9.21 

33.73 

9.35 

33.69 

9.50 

35 

36 

34.77 

9.32 

34.73 

9.47 

34.69 

9.62 

34.65 

9.77 

36 

37 

35.74 

9.58 

35.70 

9.73 

35.65 

9.89 

35.61 

10.04 

37 

38 

36.71 

9.84 

36.66 

10.00 

36.62 

10.16 

36.57 

10.31 

38 

39 

37.67 

10.09 

37.63 

10.26 

37.58 

10.42 

37.54 

10.59 

39 

40 

30.64 

10.35 

38.59 

10.52 

38.55 

10.69 

38.50 

10.86 

40 

41 

39.60 

10.61 

39.56 

10.78 

39.51 

10.96 

39.46 

11.13 

41 

42 

40.57 

10.87 

40.52 

11.05 

40.47 

11.22 

40.42 

11.40 

42 

43 

41.53 

11.13 

41.49 

11.31 

41.44 

11.49 

41.39 

11.67 

43 

44 

42.50 

11.39 

42.45 

11.57 

42.40 

11.76 

42.35 

11.94 

44 

45 

43.47 

11.65 

43.42 

11.84 

43.36 

12.03 

43.31 

12.21 

45 

46 

44.43 

11.91 

44.38 

12.10 

44.33 

12.29 

44.27 

12.49 

46 

47 

45.40 

12.16 

45.35 

12.36 

45.29 

12.56 

45.24 

12.76 

47 

48 

46.36 

12.42 

46.31' 

12.63 

46.25 

12.83 

46.20 

13.03- 

48 

49 

47.33 

12.68 

47.27 

12.89 

47.22 

13.09 

47.16 

13.30 

49 

50 

43.30 

12.94 

48.24 

13.15 

48.18 

13.36 

48.12 

13.57 

50 

o 

JkDep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

• 

o 

3 

.a. 
Q 

1 

75 Deg. 

74} Deg. 

74} Deg. 

74} Deg. 

W 

a 

+-> 

00 
• pH 

Q 





































































































TRAVERSE TABLE. 


33 


g 

r/> 

(-*■ 

P 

►3 

15 Deg. 

15} Deg. 

15} Deg. 

15} Deg. 

t) 

►-». 
c/> 
r*- 

P 

o 

n 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

p 

o 

a 

51 

49.26 

13.20 

49.20 

13.41 

49.15 

13.63 

49.09 

13.84 

51 

52 

50.23 

13.46 

50.17 

13.68 

50.11 

13.90 

50.05 

14.11 

52 

53 

51.19 

13.72 

51.13 

13.94 

51.07 

14.16 

51.01 

14.39 

53 

54 

52.16 

13.98 

52.10 

14.20 

52.04 

14.43 

51.97 

14.66 

54 

55 

53.13 

14.24 

53.06 

14.47 

53.00 

14.70 

52.94 

14.93 

55 

56 

54.09 

14.49 

54.03 

14.73 

53.96 

14.97 

53.90, 

15.20 

56 

57 

55.06 

14.75 

54.99 

14.99 

54.93 

15.23 

54.86 

15.47 

57 

58 

56.02 

15.01 

55.96 

15.26 

55.89 

15.50 

55.82 

15.74 

58 

59 

56.99 

15.27 

56.92 

15.52 

56.85 

15.77 

56.78 

16.01 

59 

60 

57.96 

15.53 

57.89 

i 

15.78 

57.82 

16.03 

57.75 

16.29 

60 

61 

58.92 

15.79 

58.85 

16.04 

58.78 

16.30 

58.71 

16.56 

61 

62 

59.89 

16.05 

59.82 

16.31 

59.75 

16.57 

59.67 

16.83 

62 

63 

60.85 

16.31 

60.78 

16.57 

60.71 

16.84 

60.63 

17.10 

63 

64 

61.82 

16.56 

61.75 

16.83 

61.67 

17.10 

61.60 

17.37 

64 

65 

62.79 

16.82 

62.71 

17.10 

62.64 

17.37 

62.56 

17.64 

65 

66 

63.75 

17.08 

63.68 

17.36 

63.60 

17.64 

63.52 

17.92 

66 

67 

64.72 

17.34 

64.64 

17.62 

64.56 

17.90 

64.48 

18.19 

67 

68 

65.68 

17.60 

65.61 

17.89 

65.53 

18.17 

65.45 

18.46 

68 

69 

66.65 

17.86 

66.57 

18.15 

66.49 

18.44 

66.41 

18.73 

69 

70 

67.61 

18.12 

67.54 

1 

18.41 

67.45 

18.71 

67.37 

19.00 

70 

71 

68.58 

18.38 

68.50 

18.68 

68.42 

18.97 

68.33 

19.27 

71 

72 

69.55 

18.63 

69.46 

18.94 

69.38 

19.24 

69.30 

19.54 

72 

73 

70.51 

18.89 

70.43 

19.20 

70.35 

19.51 

70.26 

19.82 

73 

74 

71.48 

19.15 

71.39 

19.46 

71.31 

19.78 

71.22 

20.09 

74 

75 

72.44 

19.41 

72.36 

19.73 

72.27 

20.04 

72.18 

20.36 

75 

76 

73.41 

19.67 

73.32 

19.99 

73.24 

20.31 

73.15 

20.63 

76 

77 

74.38 

19.93 

74.29 

20.25 

74.20 

20.58 

74.11 

20.90 

77 

78 

75.34 

20.19 

75.25 

20.52 

75.16 

20.84 

75.07 

21.17 

78 

79 

76.31 

20.45 

76.22 

20.78 

76.13 

21.11 

76.03 

21.44 

79 

80 

77.27 

20.71 

77.18 

21.04 

77.09 

21.38 

77.00 

21.72 

80 

81 

78.24 

20.96 

78.15 

21.31 

78.05 

21.65 

77.96 

21.99 

81 

82 

79.21 

21.22 

79.11 

21.57 

79.02 

21.91 

78.92 

22.26 

82 

83 

80.17 

21.48 

80.08 

21.83 

79.98 

22.18 

79.88 

22.53 

83 

84 

81.14 

21.74 

81.04 

22.09 

80.94 

22.45 

80.85 

22.80 

84 

85 

82.10 

22.00 

82.01 

22.36 

81.91 

22.72 

81.81 

23.07 

85 

86 

83.07 

22.26 

82.97 

22.62 

82.87 

22.98 

82.77 

23.34 

86 

87 

84.04 

22.52 

83.94 

22.88 

83.84 

23.25 

83.73 

23.62 

87 

88 

85.00 

22.78 

84.90 

23.15 

84.80 

23.52 

84.70 

23.89 

88 

89 

85.97 

23.03 

85.87 

23.41 

85.76 

23.78 

85.66 

24.16 

89 

90 

86.93 

23.29 

86.83 

23.67 

86.73 

24.05 

86.62 

24.43 

90 

91 

87.90 

23.55 

87.80 

23.94 

87. G9 

24.32 

87.58 

24.70 

91 

92 

88.87 

23.81 

88.76 

24.20 

88.65 

24.59 

88.55 

24.97 

92 

93 

89.83 

24.07 

89.73 

24.46 

89.62 

24.85 

89.51 

25.24 

93 

94 

90.80 

24.33 

90.69 

24.72 

90.58 

25.12 

90.47 

25.52 

94 

95 

91.76 

24.59 

91.65 

24.99 

91.54 

25.39 

91.43 

25.79 

95 

96 

92.73 

24.85 

92.62 

25.25 

92.51 

25.65 

92.40 

26.06 

96 

97 

93.69 

25.11 

93.58 

25.51 

93.47 

25.92 

93.36 

26.33 

97 

98 

94.66 

25.36 

94.55 

25.78 

94.44 

26.19 

94.32 

26.60 

98 

99 

95.63 

25.62 

95.51 

26.04 

95.40 

26.46 

95.28 

26.87 

99 

100 

96.59 

25.88 

96.48 

26.30 

96.36 

26.72 

96.25 

27.14 

100 

i 

<u 

o 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 1 

Lat. 

. 

0) 

o 

P 

ct5 

■*-> 

tf) 

• H 

a 

. . ..±. — 

75 Deg. 

745 Deg. 

74} Deg. 

74} Deg. 

i 

$ 

If > 

• 

3 


E 














































































34 


TRAVERSE TABLE 


d 

t— > 

to 

<“► 

P 

3 

o 

CD 

16 Deg. 

16} Deg. 

16} Deg. 

16f Deg. 

Distance. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

1 

0.96 

0.28 

0.96 

0.28 

0.96 

0.28 

0.96 

0.29 

1 

2 

1.92 

0.55 

1.92 

0.56 

1.92 

0.57 

1.92 

0.58 

2 

3 

2.88 

0.83 

2.88 

0.84 

2.88 

0.85 

2.87 

0.86 

3 

4 

3.85 

1.10 

3.84 

1.12 

3.84 

1.14 

3.83 

1.15 

4 

5 

4.81 

1.38 

4.80 

1.40 

4.79 

1.42 

4.79 

1.44 

5 

6 

5.77 

1.65 

5.76 

1.68 

5.75 

1.70 

5.75 

1.73 

6 

7 

6.73 

1.93 

6.72 

1.96 

6.71 

1.99 

6.70 

2.02 

7 

8 

7.69 

2.21 

7.68 

2.24 

7.67 

2.27 

7.66 

2.31 

8 

9 

8.65 

2.48 

8.64 

2.52 

8.63 

2.56 

8.62 

2.59 

9 

10 

9.61 

2.76 

9.60 

2.80 

9.59 

2.84 

9.58 

2.88 

10 

11 

10.57 

3.03 

10.56 

3.08 

10.55 

3.12 

10.53 

3.17 

11 

12 

11.54 

3.31 

11.52 

3.36 

11.51 

3.41 

11.49 

3.46 

12 

13 

12.50 

3.58 

12.43 

3.64 

12.46 

3.69 

12.45 

3.75 

13 

14 

13.46 

3.86 

13.44 

3.92 

13.42 

3.98 

13.41 

4.03 

14 

15 

14.42 

4.13 

14.40 

4.20 

14.38 

4.26 

14.36 

4.32 

15 

16 

15.38 

4.41 

15.36 

4.48 

15.34 

4.54 

15.32 

4.61 

16 

17 

16.34 

4.69 

16.32 

4.76 

16.30 

4.83 

16.28 

4.90 

17 

] 18 

17.30 

4.96 

17.28 

5.04 

17.26 

5.11 

17.24 

5.19 

18 

| 19 

J8.26 

5.24 

18.24 

5.32 

18.22 

5.40 

18.19 

5.48 

19 

8 20 

19.23 

5.51 

19.20 

5.60 

19.18 

5.68 

19.15 

5.76 

20 

21 

20.19 

5.79 

20.16 

5.88 

20.14 

5.96 

20.11 

6.05 

21 

OO 

.-w -w 

.21.15 

6.06 

21.12 

6.16 

21.09 

6.25 

21.07 

6.34 

22 

23 

22.11 

6.34 

22.08 

6.44 

22.05 

6.53 

22.02 

6.63 

23 

24 

23.07 

6.62 

23.04 

6.72 

23.01 

6.82 

22.98 

6.92 

24 

25 

24.03 

6.89 

24.00 

7.00 

23.97 

7.10 

23.94 

7.20 

25 

26 

24.99 

7.17 

24.96 

7.28 

24.93 

7.38 

24.90 

7.49 

26 

27 

25.95 

7.44 

25.92 

7.56 

25.89 

7.67 

25.85 

7.78 

27 

28 

26.92 

7.72 

26.88 

7.84 

26.85 

7.95 

26.81 

8.07 

28 

29 

27.88 

7.99 

27.84 

8.11 

27.81 

8.24 

27.77 

8.36 

29 

30 

28.84 

8.27 

28.80 

8.39 i 

28.76 

8.52 

28.73 

8.65 

30 

31 

29.80 

8.54 

29.76 

8.67 

29.72 

8.80 

29.68 

8.93 

31 

32 

30.76 

8.82 

30.72 

8.95 

30.68 

9.09 

30.64 

9.22 

32 

33 

31.72 

9.10 

31.68 

9.23 

31.64 

9.37 

31.60 

9.51 

33 

34 

32.68 

9.37 

32.64 

9.51 

32.60 

9.66 

32.56 

9.80 

34 

35 

33.64 

9.65 

33.60 

9.79 

33.56 

9.94 

33.51 

10.09 

35 

36 

34.61 

9.92 

34.56 

10.07 

34.52 

10.22 

34.47 

10.38 

36 

37 

35.57 

10.20 

35.52 

10.35 

35.48 

10.51 

35.43 

10.66 

37 

38 

36.53 

10.47 

36.48 

10.63 

36.44 

10.79 

36.39 

10.95 

38 

39 

37.49 

10.75 

37.44 

10.91 

37.39 

11.08 

37.35 

11.24 

39 

40 

38.45 

11.03 

38.40 

11.19 

38.35 

11.36 

38.30 

11.53 

40 

41 

39.41 

11.30 

39.36 

11.47 

39.31 

11.64 

39.26 

11.82 

41 

42 

40.37 

11.58 

40.32 

11.75 

40.27 

11.93 

40.22 

12.10 

42 

43 

41.33 

11.85 

41.28 

12.03 

41.23 

12.21 

41.18 

12.39 

43 

44 

42.30 

12.13 

42.24 

12.31 

42.19 

12.50 

42.13 

12.68 

44 

45 

43.26 

12.40 

43.20 

12.59 

43.18 

12.78 

43.09 

12.97 

45 

46 

44.22 

12.68 

44.16 

12.87 

44.11 

13.06 

44.05 

13.26 

46 

47 

45.18 

12.95 

45.12 

13.15 

45.06 

13.35 

45.01 

13.55 

47 

48 

46.14 

13.23 

46.08 

13.43 

46.02 

13.63 

45.96 

13.83 

48 

49 

47.10 

13.51 

47.04 

13.71 

46.98 

13.92 

46.92 

14.12 

49 

50 

48.06 

13.78 

48.00 

13.99 

47.94 

14.20 

47.88 

14.41 

50 

| Distance. 

Dep. | 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. | 

Lat. 

j Distance. 

1 

74 Deg. 

73| Deg. 

I 

73} Deg. 

73} Deg. 


































































































TRAVERSE TABLE 


35 


c 

u> 

r+> 

V 

16 Deg. 

16* 

Deg. 

16* 

Deg. 

16f Deg. 

0 
i—. 

GO 

ft- 

P 

o 

CO 

Lat. 

Dep. 

Lat. 

| Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

3 

O 

(0 

• 

51 

49.02 

14.06 

48.96 

14.27 

48.90 

14.48 

48.84 

14.70 

51 

52 

49.99 

14.33 

49.92 

14.55 

49.86 

14.77 

49.79 

14.99 

52 

53 

50.95 

14.61 

50.88 

14.83 

50.82 

15.05 

50.75 

15.27 

53 

54 

51.91 

14.88 

51.84 

15.11 

51.78 

15.34 

51.71 

15.56 

54 

55 

52.87 

15.16 

52.80 

15.39 

52.74 

15.62 

52.67 

15.85 

55 

56 

53.83 

15.44 

53.76 

15.67 

53.69 

15.90 

53.62 

16.14 

56 

57 

54.79 

15.71 

54.72 

15.95 

54.65 

16.19 

54.58 

16.43 

57 

58 

55.75 

15.99 

55.68 

16.23 

55.61 

16.47 

55.54 

16.72 

58 

59 

56.71 

16.26 

56.64 

16.51 

56.57 

16.76 

56.50 

17.00 

59 

60 

57.68 

16.54 

57:60 

16.79 

57.53 

17.04 

57.45 

17.29 

60 

61 

58.64 

16.81 

58.56 

17.07 

58.49 

17.32 

58.41 

17.58 

61 

62 

59.60 

17.09 

59.52 

17.35 

59.45 

17.61 

59.37 

17.87 

62 

63 

60.56 

17.37 

60.48 

17.63 

60.41 

17.89 

60.33 

18.16 

63 

; 64 

61.52 

17.64 

61.44 

17.91 

61.36 

18.18 

61.28 

18.44 

64 

; I 65 

62.48 

17.92 

62.40 

18.19 

62.32 

18.46 

62.24 

18.73 

65 j 

66 

63.44 

18.19 

63.36 

18.47 

63.28 

18.74 

63.20 

19.02 

66 1 

; 67 

64.40 

18.47 

64.32 

18.75 

64.24 

19.03 

64.16 

19.31 

67 1 

i.i 68 

65.37 

18.74 

65.28 

19.03 

65.20 

19.31 

65.11 

19.60 

$8 

1 69 

66.33 

19.02 

66.24 

19.31 

66.16 

19.60 

66.07 

19.89 

69 f 

| 70 

67.29 

19.29 

.... ! 

67.20 

19.59 

67.12 

19.88 

67.03 

20.17 

70 'i 

1 71 

68.25 

19.57 

68.16 

19.87 

68.08 

20.17 

67.99 

20.46 

71 1 

f 72 

69.21 

19-85 

69.12 

20.15 

69.03 

20.45 

68.95 

20.75 

72 

S 73 

70.17 

20.12 

70.08 

20.43 

69.99 

20.73 

69.90 

21.04 

73 1 

I 74 

71.13 

20.40 

71.04 

20.71 

70.95 

21.02 

70.86 

21.33 

'74 j 

I 75 

72-09 

20.67 

72.00 

20.99 

71.91 

21.30 

71.82 

21.61 

75 

g ot 

| / a 

73.06 

20.95 

72.96 

21.27 

72.87 

21.59 

72.78 

21.90 

76 j 

1 77 

74.02 

21.22 

73.92 

21.55 

73.83 

21.87 

73.73 

22.19 

77 i 

1 78 

74.98 

21.50 

74.88 

21.83 

74.79 

22.15 

74.69 

22.48 

78 j 

1 79 

75.94 

21.78 

75.84 

22.11 

75.75 

22.44 

75.65 

22.77 

79 

1 80 

76.90 

22.05 

76.80 

22.39 

76.71 

22.72 

76.61 

23.06 

80 

■ 

81 

77.86 

22.33 

77.76 

22.67 

77.66 

23.01 

77.56 

23.34 

81 j 

i 1 82 

78.82 

22.60 ' 

73.72 

22.95 

78.62 

23.29 

78.52 

23.63 

82 ! 

83 

79.78 

22.88 

79.68 

23.23 

79.58 

23.57 

79.48 

23.92 

83 ; 

84 

80.75 

23.15 

80.64 

23.51 

80.54 

23.86 

80.44 

24.21 

84 : 

1 85 

81.71 

23.43 

81.60 

23.79 

81.50 

24.14 

81.39 

24.50 

85 

i 86 

82.67 

23.70 

82.56 

24.07 

82.46 

24.43 

82.35 

24.78 

86 

87 

83.63 

23.98 

83.52 

24.35 

83.42 

24.71 

83.31 

25.07 

87 

88 

84.59 

24.26 

84.48 

24.62 

84.38 

24.99 

84.27 

25.36 

88 I 

I 89 

85.55 

24.53 

85.44 

24.90 

85.33 

25.28 

85.22 

25.65 

89 | 

j 90 

86.51 

24.81 

35.40 

25.18 ' 

86.29 

25.56 : 

-_ Lm __ | 

86.18 

25.94 

90 j| 

■ 91 

87.47 

25.08 

87.36 

25.46 j 

87.25 

25.85 | 

87.14 

26.23 

91 

92 

88.44 

25.36 

88.32 

25.74 j 

88.21 

26.13 

88.10 

26.51 

92 | 

93 

89.40 

25.63 i 

89.28 

26.02 i 

89.17 

26.41 

89.05 

26.80 

* 

94 

90.36 

25.91 

90.24 

26.30 ! 

90.13 

26.70 

90.01 

27.09 

94 ] 

95 

91.32 

26.19 

91.20 

26.58 ! 

91.09 

26.98 

90.97 

27.38 

95 

96 

92.28 

26.46 |; 

92.16 

26.86 i| 

92.05 

27.27 

91.93 

27.67 

96 

97 

93.24 

26.74 |i 

93.12 

27.14 

93.01 

27.55 ! 

92.88 

27.95 

97 

98 

94.20 

27.01 j 

94.08 

27.42 

93.96 

27.83 1 

93.84 

28.24 

98 

99 

95.16 

27.29 

95.04 

27.70 

94.92 

28.12 | 

94.80 

28.53 

99 || 

100 

96.13 

27.56 

96.00 

27.98 | 

95.88 

28.40 ! 

i 

95.76 

28.82 

100 

■ ■■■■-—[ 

o 

o 

Dep. 

Lat. I 

I 

Dep. 1 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

ol 

o 

a 

ct 

'ft 

Q 

74 Deg. 

73* Deg. 

73* Deg. 

i 

73* Deg. 

(ft 

5 




































































































































36 


TRAVERSE TARLE. 


Distance. 

17 Deg. 

17} Deg. 

17} Deg. 

17} Deg. 1 

0 
h- . 

u> 

<-*- 

p 

C3 

O 

<6 

• 

Lat. 

Dep. 

Lat. 

Dep. 

1 

Lat. 

Dep. 

Lat. 

Dep. 

1 

0.96 

0.29 

0.95 

0.30 

0.95 

0.30 

0.95 

0.30 

1 

2 

1.91 

0.58 

1.91 

0.59 

1.91 

0.60 

1.90 

0.61 

2 

3 

2.87 

0.88 

2.87 

0.89 

2.86 

0.90 

2.86 

0.91 

3 

4 

3.83 

1.17 

3.82 

1.19 

3.81 

1.20 

3.81 

1.22 

4 

5 

4.78 

1.46 

4.78 

1.48 

4.77 

1.50 

4.76 

1.52 

5 

6 

5.74 

1.75 

5.73 

1.78 

5.72 

1.80 

5.71 

1.83 

6 

7 

6.69 

2.05 

6.69 

2.08 

6.68 

2.10 

6.67 

2.13 

7 

8 

7.65 

2.34 

7.64 

2.37 

7.63 

2.41 

7.62 

2.44 

8 

9 

8.61 

2.63 

8.60 

2.67 

8.58 

2.71 

8.57 

2.74 

9 

to 

9.56 

2.92 

9.55 

2.97 

9.54 

3.01 

9.52 

3.05 

10 

11 

10.52 

3.22 

10.51 

3.26 

10.49 

3.31 

10.48 

3.35 

11 

12 

11.48 

3.51 

11.46 

3.56 i 

11.44 

3.61 

11.43 

3.66 

12 

13 

12.43 

3.80 

12.42 

3.85 I 

12.40 

3.91 

12.38 

3.96 

13 

14 

13.39 

4.09 

13.37 

4.15 ! 

13.35 

4.21 

13.33 

4.27 

14 

15 

14.34 

4.39 

14.33 

4.45 

14.31 

4.51 

14.29 

4.57 

15 

16 

15.30 

4.68 

15.*28 

4.74 

15.26 

4.81 

15.24 

4.88 

16 

17 

16.26 

4.97 

16.24 

5.04 

16.21 

5.11 

16.19 

5.18 

17 

18 

17.21 

5.26 

17.19 

5.34 

17.17 

5.41 

17.14 

5.49 

18 

19 

18.17 

5.56 

18.15 

5.63 

18.12 

5.71 

18.10 

5.79 

19 

20 

19.13 

5.85 

19.10 

5.93 

| 

19.07 

6.01 

19.05 

i. 

6.10 

20 

21 

20.08 

6.14 

20.06 

6.23 

1 

20.03 

6.31 

20.00 

6.40 

21 

22 

21.04 

6.43 

21.01 

6.52 

20.98 

6.62 

20.95 

6.71 

22 

23 

21.99 

6.72 

21.97 

6.82 

21.94 

6.92 

21.91 

7.01 

23 

24 

22.95 

7.02 

22.92 

7.12 | 

22.89 

7.22 

22.86 

7.32 

24 

25 

23.91 

7.31 

23.88 

7.41 1 

23.84 

7.52 

23.81 

7.62 

25 

26 

24.86 

7.60 

24.83 

7.71 

24.80 

7.82 

24.76 

7.93 

26 

27 

25.82 

7.89 

25.79 

8.01 

25.75 

8.12 

25.71 

8.23 

27 

! 28 

26.78 

8.19 

26.74 

8.30 

26.70 

8.42 

26.67 

8.54 

28 

29 

27.73 

8.48 

27.70 

8.60 

27.66 

8.72 

27.62 

8.84 

29 

30 

28.69 

8.77 

28.65 

8.90 

28.61 

9.02 

28.57 

9.15 

30 

31 

29.65 

9.06 

29.61 

9.19 

29.57 

9.32 

29.52 

9.45 

31 

32 

30.60 

9.36 

30.56 

9.49 

30.52 

9.62 

30.48 

9.76 

32 

33 

31.56 

9.65 

31.52 

9.79 

31.47 

9.92 

31.43 

10.06 

33 

34 

32.51 

9.94 

32.47 

10.08 

32.43 

10.22 

32.38 

10.37 

34 

35 

33.47 

10.23 

33.43 

10.38 

33.38 

10.52 

33.33 

10.67 

35 

36 

34.43 

10.53 

34.38 

10.68 

34.33 

10.83 

34.29 

10.98 

36 

37 

35.38 

10.82 

35.34 

10.97 

35.29 

11.13 

35.24 

11.28 

37 

38 

36.34 

11.11 

36.29 

11.27 

36.24 

11.43 

36.19 

11.58 

38 

39 

37.30 

11.40 

37.25 

11.57 

37.19 

11.73 

37.14 

11.89 

39 

40 

38.25 

11.69 

38.20 

11.86 

38.15 

12.03 

38.10 

12.19 

40 

41 

39.21 

11.99 

39.16 

12.16 

39.10 

12.33 

39.05 

12.50 

41 

42 

40.16 

12.28 

40.11 

12.45 

40.06 

12.63 

40.00 

12.80 

42 

43 

41.12 

12.57 

41.07 

12.75 

41.01 

12.93 

40.95 

13.11 

43 

44 

42.08 

12.86 

42.02 

13.05 

41.96 

13.23 

41.91 

13.41 

44 

45 

43.03 

13.16 

42.98 

13.34 

42.92 

13.53 

42.86 

13.72 

45 

46 

43.99 

13.45 

43.93 

13.64 

43.87 

13.83 

43.81 

14.02 

46 

47 

44.95 

13.74 

44.89 

13.94 

44.82 

14.13 

44.76 

14.33 

47 

48 

45.90 

14.03 

45-84 

14.23 

45.78 

14.43 

45.71 

14.63 

48 

49 

46.86 

14.33 

46.80 

14.53 

46.73 

14.73 

46.67 

14.94 

49 

50 

47.82 

14.62 

47.75 

14.83 

j 47.69 

15.04 

47.62 

15.24 

50 

1 Distance. 

Dep. 

Lat. 

Dep. 

Lat. 

| Dep. 

Lat. 

Dep. 

Lat. 

--- 

Distance. 

73 Deg. 

73} Deg. 

1 

72i Deg. 

1 

72} Deg. 

1 








































































































TRAVERSE TABLE 


37 


o 

UD* 

2 

17 Deg. 

17* Deg. 

17* Deg. 

, 17| Deg. | 

G 

n 

o 

c& 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

p 

o 

a 

51 

48.77 

14.91 

48.71 

15.12 

48.64 

15.34 

48.57 

15.55 

51 

52 

49.73 

15.20 

49.66 

15.42 

49.59 

15.64 

49.52 

15.85 

52 

53 

50.68 

15.50 

50.62 

15.72 

50.55 

15.94 

50.48 

16.16 

53 

54 

51.64 

15.79 

51.57 

16.01 

51.50 

16.24 

51.43 

16.46 

54 

55 

52.60 

16.08 

52.53 

16.31 

52.45 

16.54 

52.38 

16.77 

55 

56 

53.55 

16.37 

53.48 

16.61 

53.41 

16.84 

53.33 

17.07 

56 

57 

54.51 

16.67 

54.44 

16.90 

54.36 

17.14 

54.29 

17.38 

57 

58 

55.47 

16.96 

55.39 

17.20 

55.32 

17.44 

55.24 

17.68 

58 

59 

56.42 

17.25 

56.35 

17.50 

56.27 

17.74 

56.19 

17.99 

59 

60 

57.38 

17.54 

57.30 

17.79 

57.22 

18.04 

57.14 

18.29 

60 

61 

58.33 

17.83 

58.26 

18.09 

58.18 

18.34 

58.10 

18.60 

61 

62 

59.29 

18.13 

59.21 

18.39 

59.13 

18.64 

59.05 

18.90 

62 

63 

60.25 

18.42 

60.17 

18.68 

60.08 

18.94 

60.00 

19.21 

63 

64 

61.20 

18.71 

61.12 

18.98 

61.04 

19.25 

60.95 

19.51 

64 

65 

62.16 

19.00 

£2,08 

19.28 

61.99 

19.55 

61.91 

19.82 

65 

66 

63.12 

19.30 

63.03 

19.57 

62.95 

19.85 

62.86 

20.12 

66 

67 

64.07 

19.59 

63.99 

19.87 

63.90 

20.15 

63.81 

20.43 

67 

68 

65.03 

19.88 

64.94 

20.16 

64.85 

20.45 

64.76 

20.73 

68 

69 

65.99 

20.17 

65.90 

20.46 

65.81 

20.75 

65.72 

21.04 

69 

70 

66.94 

20.47 

66.85 

20.76 

66.76 

21.05 

66.67 

21.34 

70 

71 

67.90 

20.76 

67.81 

21.05 

67.71 

21.35 

67.62 

21.65 

71 

72 

68.85 

21.05 

68.76 

21.35 

68.67 

21.65 

68.57 

21.95 

72 

73 

69.81 

21.34 

69.72 

21.65 

69.62 

21.95 

69.52 

22.26 

73 

74 

70.77 

21.64 

70.67 

21.94 

70.58 

22.25 

70.48 

22.56 

74 

75 

71.72 

21.93 

71.63 

22.24 

71.53 

22.55 

71.43 

22.86 

75 

76 

72.68 

22.22 

72.58 

22.54 

72.48 

'22.85 

72.38 

23.17 

76 

77 

73.64 

22.51 

73.54 

22.83 

73.44 

23.15 

73.33 

23.47 

77 

78 

74.59 

22.80 

74.49 

23.13 

74.39 

23.46 

74.29 

23.78 

78 

79 

75.55 

23.10 

75.45 

23.43 

75.34 

23.76 

75.24 

24.08 

79 

80 

76.50 

23.39 

76.40 

23.72 

76.30 

24.06 

76.19 

24.39 

80 

81 

77.46 

23.68 

77.36 

24.02 

77.25 

24.36 

77.14 

24.69 

81 

82 

78.42 

23.97 

78.31 

24.32 

78.20 

24.66 

78.10 

25.00 

82' 

83 

79.37 

24.27 

79.27 

24.61 

79.16 

25.96 

79.05 

25.30 

83 

84 

80.33 

24.56 

80.22 

24.91 

80.11 

25.26 

80.00 

25.61 

84 

85 

81.29 

24.85 

81.18 

25.21 

81.07 

25.56 

80.95 

25.91 

85 

86 

82.24 

25.14 

82.13 

25.50 

82.02 

25.86 

81.91 

26.22 

86 

87 

83.20 

25.44 

83.09 

25.80 

82.97 

26.16 

82.86 

26.52 

87 

88 

84.15 

25.73 

84.04 

26.10 

83.93 

26.46 

83.81 

26.83 

88 

89 

85.11 

26.02 

85.00 

26.39 

84.88 

26.76 

84.76 

27.13 

89 

90 

86.07 

26.31 

85.95 

26.69 

85.83 

27.06 

85.72 

27.44 

90 

91 

87.02 

26.61 

86.91 

26.99 

86.79 

27.36 

86.67 

27.74 

91 

92 

87.98 

26.90 

87.86 

27.28 

87.74 

27.66 

87.62 

28.05 

92 

93 

88.94 

27.19 

88.82 

27.58 

88.70 

27.97 

88.57 

28.35 

93 

94 

89.89 

27.48 

89.77 

27.87 

89.65 

28.27 

89.53 

28.66 

94 

95 

90.85 

27.78 

90.73 

28.17 

90.60 

28.57 

90.48 

28.96 

95 

96 

91.81 

28.07 

91.68 

28.47 

91.56 

28.87 

91.43 

29.27 

96 

97 

92.76 

28.36 

92.64 

28.76 

92.51 

29.17 

92.38 

29.57 

97 

98 

93.72 

28.65 

93.59 

29.06 

93.46 

29.47 

93.33 

29.88 

98 

99 

94.67 

28.94 

94.55 

29.36 

94.42 

29.77 

94.29 

30.18 

99 

100 

95.63 

29.24 I 

95.50 

29.65 

95.37 

30.07 

95.24 

30.49 

100 

ol 

o 

Dep. 

L(it« 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

4> 

O 

c 

c 

a 

a* 

• pH 

Q 

73 Deg. 

i 

721 Beg. 

72* Deg. 

72* Deg. 

ci 

.2 

c 


































































































38 


TRAVERSE TABLE 


a 

to’ 

r-+- 

P 

18 Deg. 

18* 

Deg. 

m 

Deg. 

18| Deg. 

0 

C*" 

P{ 

S 

s 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

o 

CD 

1 

0.95 

0.31 

0.95 

0.31 

0.95 

0.32 

0.95 

0.32 

1 

2 

1.90 

0.62 

1.90 

0.63 

1.90 

0.63 

1.89 

0.64 

2 

3 

2.85 

0.93 

2.85 

0.94 

2.84 

0.95 

2.84 

0.96 

3 

4 

3.80 

1.24 

3.80 

1.25 

3.79 

1.27 

3.79 

1.29 

4 

5 

4.76 

1.55 

4.75 

1.57 

4.74 

1.59 

4.73 

1.61 

5 

6 

5.71 

1.85 

5.70 

1.88 

5.69 

1.90 

5.68 

1.93 

6 

7 

6.66 

2.16 

6.65 

2.19 

6.64 

2.22 

6.63 

2.25 

7 

8 

7.61 

2.47 

7.60 

2.51 

7.59 

2.54 

7.58 

2.57 

8 

9 

8.56 

2.78 

8.55 

2.82 

8.53 

2.86 

8.52 

2.89 

9 

10 

9.51 

3.09 

9.50 

3.13 

9.48 

3.17 

9.47 

3.21 

10 

11 

10.46 

3.40 

10.45 

3.44 

10.43 

3.49 

10.42 

3.54 

11 

12 

11.41 

3.71 

11.40 

3.76 

11.38 

3.81 

11.36 

3.86 

12 

13 

12.36 

4.02 

12.35 

4.07 

12.33 

4.12 

12.31 

4.18 

13 

14 

13.31 

4.33 

13.30 

4.38 

13.28 

4.44 

13.26 

4.50 

14 

15 

14.27 

4.64 

14.25 

4.70 

14.22 

4.76 

14.20 

4.82 

15 

16 

15.22 

4.94 

15.20 

5.01 

15.17 

5.08 

15.15 

5.14 

16 

17 

16.17 

5.25 

16.14 

5.32 

16.12 

5.39 

16.10 

5.46 

17 

18 

17.12 

5.56 

17.09 

5.64 

17.07 

5.71 

17.04 

5.79 

18 

19 

18.07 

5.87 

18.04 

5.95 

18.02 

6.03 

17.99 

6.11 

19 

20 

19.02 

6.18 

18.99 

6.26 

18.97 

6.35 

18.94 

6.43 

20 

21 

19.97 

6.49 

19.94 

6.58 

19.91 

6.66 

19.89 

6.75 

21 

22 

20.92 

6.80 

20.89 

6.89 

20.86 

6.98 

20.83 

7.07 

22 

23 

21.87 

7.11 

21.84 

7.20 

21.81 

7.30 

21.78 

7.39 

23 

24 

22.83 

7.42 

22.79 

7.52 

22.76 

7.62 

22.73 

7.71 

24 

25 

23.78 

7.73 

23.74 

7.83 

23.71 

7.93 

23.67 

8.04 

25 

26 

24.73 

8.03 

24.69 

8.14 

24.66 

8.25 

24.62 

8.36 

26 

27 

25.68 

8.34 

25.64 

8.46 

25.60 

8.57 

25.57 

8.68 

27 

28 

26.63 

8.65 

26.59 

8.77 

26.55 

8.88 

26.51 

9.00 

28 

29 

27.58 

8.96 

27.54 

9.08 

27.50 

9.20 

27.46 

9.32 

29 

30 

28.53 

9.27 

28.49 

9.39 

28.45 

9.52 

28.41 

9.64 

30 

31 

29.48 

9.58 

29.44 

9.71 

29.40 

9.84 

29.35 

9.96 

31 

32 

30.43 

9.89 

30.39 

10.02 

30.35 

10.15 

30.30 

10.29 

32 

33 

31.38 

10.20 

31.34 

10.33 

31.29 

10.47 

31.25 

10.61 

33 

34 

32.34 

10.51 

32.29 

10.65 

32.24 

10.79 

32.20 

10.93 

34 

35 

33.29 

10.82 

33.24 

10.96 

33.19 

11.11 

33.14 

11.25 

35 

36 

34.24 

11.12 

34.19 

11.27 

34.14 

11.42 

34.09 

11.57 

36 

37 

35.19 

11.43 

35.14 

11.59 

35.09 

11.74 

35.04 

11.89 

37 

38 

36.14 

11.74 

36.09 

11.90 

36.04 

12.06 

35.98 

12.21 

38 

39 

37.09 

12.05 

37.04 

12.21 

36.98 

12.37 

36.93 

12.54 

39 

40 

38.04 

12.36 

37.99 

12.53 

37.93 

12.69 

37.88 

12-86 

40 

41 

38.99 

12.67 

38.94 

12.84 

38.88 

13.01 

38.82 

13.18 

41 

42 

39.94 

12.98 

39.89 

13.15 

39.83 

13.33 

39.77 

13.50 

42 

43 

40.90 

13.29 

40.84 

13.47 

40.78 

13.64 

40.72 

13.82 

43 

44 

41.85 

13.60 

41.79 

13.78 

41.73 

13.96 

41.66 

14.14 

44 

45 

42.80 

13.91 

42.74 

14.09 

42.67 

14.28 

42.61 

14.46 

45 

46 

43.75 

14.21 

43.69 

14.41 

43.62 

14.60 

43.56 

14.79 

46 

47 

44.70 

14.52 

44.64 

14.72 

44.57 

14.91 

44.51 

15.11 

47 

48 

45.65 

14.83 

45.59 

15.03 

45.52 

15.23 

45.45 

15.43 

48 

49 

46.60 

15.14 

46.54 

15.35 

46.47 

15.55 

46.40 

15.75 

48 

50 

47.55 

15.45 

47.48 

15.66 

47.42 

15.87 

47.35 

16.07 

50 

o 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 1 

Lat. 

© 

o 

<n 

• ^ 

72 Deg. 

711 

Deg. 

7li Deg. 

71* Deg. 

3 

C/5 

Q 






















































































TRAVERSE TABLE 


39 


1 Distance. 1 

1 1 

18 Deg. 

184 Deg. 

18£ Deg. 

18| Deg. 

d 

w 

sr 

3 

O 

? 

Lat. 

Dep. 

Lat. 

! -—— 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

51 

48.50 

15.76 

48.43 

15.97 

48.36 

16.18 

48.29 

16.39 

51 

52 

49.45 

16.07 

49.38 

16.28 

49.31 

16.50 

49.24 

16.71 

52 

53 

50.41 

16.38 

50.33 

16.60 

50.26 

16.82 

50.19 

17.04 

53 

54 

51.36 

16.69 

51.28 

16.91 

51.21 

17.13 

51.13 

17.36 

54 

55 

52.31 

17.00 

52.23 

17.22 

52.16 

17.45 

52.08 

17.68 

55 

56 

53.26 

17.30 

53.18 

17.54 

53.11 

17.77 

53.03 

18.00 

56 

57 

54.21 

17.61 

54.13 

17.85 

54.05 

18.09 

53.98 

18.32 

57 

' 58 

55.16 

17.92 

55.08 

18.16 

! 55.00 

18.40 

54.92 

18.64 

58 

59 

56.11 

18.23 

56.03 

18.48 

1 55.95 

18.72 

55.87 

18.96 

59 

60 

57.06 

18.54 

56.98 

18.79 

56.90 

19.04 

56.82 

19.29 

60 

61 

58.01 

18.85 

57.93 

19.10 

57.85 

19.36 

57.76 

19.61 

61 

62 

58.97 

19.16 

58.88 

19.42 

58.80 

19.67 

58.71 

19.93 

62 

63 

59.92 

19.47 

59.83 

19.73 

59.74 

19.99 

59.66 

20.25 

63 

64 

60.87 

19.78 

60.78 

20.04 

60.69 

20.31 

60.60 

20.57 

64 

65 

61.82 

20.09 

61.73 

20.36 

61.64 

20.62 

61.55 

20.89 

65 

66 

62.77 

20.40 

62.68 

20.67 

62.59 

20.94 

62.50 

21.22 

66 

67 

63.72 

20.70 

63.63 

20.98 

63.54 

21.26 

63.44 

21.54 

67 

68 

64.67 

21.01 

64.58 

21.30 

64.49 

21.58 

64.39 

21.86 

68 

69 

65.62 

21.32 

65.53 

21.61 

65.43 

21.89 

65.34 

22.18 

69 

70 

66.57 

21.63 

66.48 

1 

21.92 

66.38 

22.21 

66.29 

22.50 

70 

71 

67.53 

21.94 

67.43 

22.23 

67.33 

22.53 

67.23 

22.82 

71 

72 

68.48 

22.25 

1 68.38 

22.55 

68.28 

22.85 

68.18 

23.14 

72 

73 

69.43 

22.56 

! 69.33 

22.86 

69.23 

23.16 

69.13 

23.47 

73 

74 

70.38 

22.87 

70.28 

23.17 

70.18 

23.48 

70.07 

23.79 

74 

75 

71.33 

23.18 

71.23 

23.49 

71.12 

23.80 

71.02 

24.11 

75 

76 

72.28 

23.49 

72.18 

23.80 

72.07 

24.12 

71.97 

24.43 

76 

( 4 

73.23 

23.79 

73.13 

24.11 

73.02 

24.43 

72.91 

24.75 

77 

78 

74.18 

24.10 

74.08 

24.43 

73.97 

24.75 

73.86 

25.07 

78 

79 

75.13 

24.41 

75.03 

24.74 

74.92 

25.07 

74.81 

25.39 

79 

80 

76.08 

24.72 

75.98 

| 

25.05 

75.87 

25.38 

75.75 

25.72 

80 

81 

77.04 

25.03 

76.93 

25.37 

76.81 

25.70 

76.70 

26.04 

81 

82 

77.99 

25.34 

77.88 

25.68 | 

77.76 

26.02 

77.65 

26.36 

82 

83 

78.94 

25.65 

78.83 

25.99 

78.71 

26.34 

78.60 

26.68 

83 

84 

79.89 

25.96 

79.77 

26.31 

79.66 

26.65 

79.54 

27.00 

84 

85 

80.84 

26.27 

80.72 

26.62 

80.61 

26.97 

80.49 

27.32 

85 

86 

81.79 

26.58 

81.67 

26.93 

81.56 

27.29 

81.44 

27.64 

86 

87 

82.74 

26.88 

82.62 

27.25 

82.50 

27.61 

82.38 

27.97 

87 

88 

83.69 

27.19 

83.57 

27.56 

83.45 

27.92 

83.33 

28.29 

88 

89 

84.64 

27.50 

84.52 

27.87 

84.40 

28.24 

84.28 

28.61 

89 

90 

85.60 

27.81 

85.47 

28.18 

85.35 

28.56 

85.22 

28.93 

90 

91 

86.55 

28.12 

86.42 

28.50 

86.30 

28.87 

86.17 

29.25 

91 

92 

87.50 

28.43 

87.37 

28*81 

87.25 

29.19 

87.12 

29.57 

92 

93 

88.45 

28.74 

88.32 

29.12 

88.19 

29.51 

88.06 

29.89 

93 

94 

89.40 

29.05 

89.27 

29.44 

89.14 

29.83 

89.01 

30.22 

94 

95 

90.35 

29.36 

90.22 

29.75 

90.09 

30.14 

89.96 

30.54 

95 

96 

91.30 

29.67 

91.17 

30.06 

91.04 

30.46 

90.91 

30.8*6 

96 

97 

92.25 

29.97 

92.12 

30.38 

91.99 

30.78 

91.85 

31.18 

97 

98 

93.20 

30.28 

93.07 

30.69 

92.94 

31.10 

92.80 

31.50 

98 

99 

94.15 

30.59 

94.02 

3i.00 

93.88 

31.41 

93.75 

31.82 

99 

100 

95.11 

30.90 

94.97 

31.32 

.... I 

94.83 

31.73 

9.4.69 

32.14 

100 

Distance. 

i 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

t)ep. 

Lat. 

6 

o 

a 

d 

C/J 

ry 

72 Deg. 

7!f Deg. 

7U Deg. 

714 Deg. 
















































































































40 


TRAVERSE TABLE 


d 

i— < • 

CD 

f-t* 

V 

19 Deg. 

194 Deg. 

19* Deg. 

19| Deg. 

d 

M • 

CD 

<-»* 

3 

O 

(D 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

o 

9 

1 

0.95 

0.33 

0.94 

0.33 

0.94 

0.33 

0.94 

0.34 

1 

2 

1.89 

0.65 

1.89 

0.66 

1.89 

0.67 

1.88 

0.68 

2 

3 

2.84 

0.98 

2.83 

0.99 

2.83 

1.00 

2.82 

1.01 

3 

4 

3.78 

1.30 

3.78 

1.32 

3.77 

1.34 

3.76 

1.35 

4 

5 

4.73 

1.63 

4.72 

1.65 

4.71 

1.67 

4.71 

1.69 

5 

6 

5.67 

1.95 

5.66 

1.98 

5.66 

2.00 

5.65 

2.03 

6 

7 

6.62 

2.28 

6.61 

2.31 

6.60 

2.34 

6.59 

2.37 

7 

8 

7.56 

2.60 

7.55 

2.64 

7.54 

2.67 

7.53 

2.70 

8 

9 

8.51 

2.93 

8.50 

2.97 

8.48 

3.00 

8.47 

3.04 

9 

10 

9.46 

3.26 

9.44 

3.30 

9.43 

3.34 

9.41 

3.38 

10 

11 

10.40 

3.58 

10.38 

3.63 

10.37 

3.67 

10.35 

3.72 

11 

12 

11.35 

3.91 

11.33 

3.96 

11.31 

4.01 

11.29 

4.06 

12 

13 

12.29 

4.23 

12.27 

4.29 

12.25 

4.34 

12.24 

4.39 

13 

14 

13.24 

4.56 

13.22 

4.62 

13.20 

4.67 

13.18 

4.73 

14 

15 

14.18 

4.88 

14.16 

4.95 

14.14 

5.01 

14.12 

5.07 

15 

16 

15.13 

5.21 

15.11 

5.28 

15.08 

5.34 

15.06 

5.41 

16 

17 

16.07 

5.53 

16.05 

5.60 

16.02 

5.67 

16.00 

5.74 

17 

18 

17.02 

5.86 

16.99 

5.93 

16.97 

6.01 

16.94 

6.08 

18 

19 

17.96 

6.19 

17.94 

6.26 

17.91 

6.34 

17.88 

6.42 

19 

20 

18.91 

6.51 

18.88 

6.59 

18.85 

6.68 

18.82 

6.76 

20 

21 

19.86 

6.84 

19.83 

6.92 

19.80 

7.01 

19.76 

7.10 

21 

22 

20.80 

7.16 

20.77 

7.25 

20.74 

7.34 

20.71 

7.43 

22 

23 

21.75 

7.49 

21.71 

7.58 

21.68 

7.68 

21.65 

7.77 

23 

24 

22.69 

7.81 

22.66 

7.91 

22.62 

8.01 

22.59 

8.11 

24 

25 

23.64 

8.14 

23.60 

8.24 

23.57 

8.35 

23.53 

8.45 

25 

26 

24.58 

8.46 

24.55 

8.57 

24.51 

8.68 

24.47 

8.79 

26 

27 

25.53 

8.79 

25.49 

8.90 

25.45 

9.01 

25.41 

9.12 

27 

28 

26.47 

9.12 

26.43 

9.23 

26.39 

9.35 

26.35 

9.46 

28 

29 

27.42 

9.44 

27.38 

9.56 

27.34 

9.68 

27.29 

9.80 

29 

30 

28.37 

9.77 

28.32 

9.89 

28.28 

10.01 

28.24 

10.14 

30 

31 

29.31 

10.09 

29.27 

10.22 

29.22 

10.35 

29.18 

10.48 

31 

32 

30.26 

10.42 

30.21 

10.55 

30.16 

10.68 

30.12 

10.81 

32 

33 

31.20 

10.74 

31.15 

10.88 

31.11 

11.02 

31.06 

11.15 

33 

34 

32.15 

11.07 

32.10 

11.21 

32.05 

11.35 

32.00 

11.49 

34 

35 

33.09 

11.39 

33.04 

11.54 

32.99 

11.68 

32.94 

11.83 

35 

36 

34.04 

11.72 

33.99 

11.87 

33.94 

12.02 

33.88 

12.17 

36 

37 

34.98 

12.05 

34*93 

12.20 

34.88 

12.35 

34.82 

12.50 

37 

38 

35.93 

12.37 

35.88 

12.53 

35.82 

12.68 

35.76 

12.84 

38 

39 

36.88 

12.70 

36.82 

12.86 

36.76 

13.02 

36.71 

13.18 

39 

40 

37.82 

13.02 

37.76 

13.19 

37.71 

13.35 

37.65 

13.52 

40 

41 

38.77 

13.35 

38.71 

13.52 

38.65 

13.69 

38.59 

13.85 

41 

42 

39.71 

13.67 

39.65 

13.85 

39.59 

14.02 

39.53 

14.19 

42 

43 

40.66 

14.00 

40.60 

14.18 

40.53 

14.35 

40.47 

14.53 

43 

44 

41.60 

14.32 

41.54 

14.51 

41.48 

14.69 

41.41 

14.87 

44 

45 

42.55 

14.65 

42.48 

14.84 

42.42 

15.02 

42.35 

15.21 

45 

46 

43 49 

14.98 

43.43 

15.17 

43.36 

15.36 

43.29 

15.54 

46 

47 

44.44 

15.30 

44.37 

15*50 

44.30 

15.69 

44.24 

15.88 

47 

48 

45.38 

15.63 

45.32 

15.83 

45.25 

16.02 

45.18 

16.22 

48 

49 

46.33 

15*95 

46.26 

16.15 

46.19 

16.36 

46.12 

16.56 

49 

50 

47.28 

16.28 

47.20 

16.48 

47.13 

16.69 

47.06 

16.90 

50 

• 

o 

o 

c 

Dep. 

Lat* 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

• 

V 

o 

CT5 

CD 

Q 

71 Deg. 

O 

70f Deg. 

i 

70* Deg. i 

i 

70* Deg. 

d 

■4~> 

c n 

• 

Q 


















































































TRAVERSE TABLE 


41 


J| Distance, j 

19 Deg. 

. . . 

19} Deg. 

1 

19} Deg. 

19i Deg. 

0 

H« 

W 

C** 

P 

s 

o 

a> 

• 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

51 

48.22 

16.60 

48.15 

16.81 

48.07 

17.02 

48.00 

17.23 

51 

52 

49.17 

16.93 

49.09 

17.14 

49.02 

17.36 

48.94 

17.57 

52 

53 

50.11 

17.26 

50.04 

17.47 

49.96 

17.69 

49.88 

17.91 

53 

54 

51.06 

17.58 

50.98 

17.80 

50.90 

18.03 

50.82 

18*25 

54 

55 

52.00 

17.91 

51.92 

18.13 

51.85 

18.36 

51.76 

18.5a 

55 

56 

52.95 

18.23 

52.87 

18.46 

52.79 

18.69 

52.71 

18.92 

56 

57 

53.89 

18.56 

53.81 

18.79 

53.73 

19.03 

53.65 

19.26 

57 

58 

54.84 

18.88 

54.76 

19.12 

54.67 

19.36 

54.59 

19.60 

58 

59 

55.79 

19.21 

55.70 

19.45 

55.62 

19.69 

55.53 

19.94 

59 

60 

56.73 

19.53 

56.65 

19.78 

56.56 

20.03 

56.47 

20.27 

60 

61 

57.68 

19.86 

57.59 

20.11 

57.50 

20.36 

57.41 

20.61 

61 

62 

58.62 

20.19 

58.53 

20.44 

58.44 

20.70 

58.35 

20.95 

62 

63 

59.57 

20.51 

59.48 

20.77 

59.39 

21.03 

59.29 

21.29 

63 

64 

60.51 

20.84 

60.42 

21.10 

60.33 

21.36 

60.24 

21.63 

64 

65 

61.46 

21.16 

61.37 

21.43 

61.27 

21.70 

61.18 

21.96 

65 

66 

62.40 

21.49 

62.31 

21.76 

62.21 

22.03 

62.12 

22.30 

66 

67 

63.35 

21.81 

63.25 

22.09 

63.16 

22.37 

63.06 

22.64 

67 

68 

64.30 

22.14 

64.20 

22.42 

64.10 

22.70 

64.00 

22.98 

68 

69 

65.24 

22.46 

65.14 

22.75 

65.04 

23.03 

64.94 

23.32 

69 

70 

66.19 

22.79 

66.09 

23.08 

65.98 

23.37 

65.88 

23.65 

70 

71 

67.13 

23.12 

67.03 

23.41 

66.93 

23.70 

66.82 

23.99 

71 

72 

68.08 

23.44 

67.97 

23.74 

67.87 

24.03 

67.76 

24.33 

72 

73 

69.02 

23.77 

68.92 

24.07 

68.81 

24.37 

68.71 

24.67 

73 

74 

69.97 

24.09 

69.86 

24.40 

69.76 

24.70 

69.65 

25.01 

74 

75 

70.91 

24.42 

70.81 

24.73 

70.70 

25.04 

70.59 

25.34 

75 

76 

71.86 

24.74 

71.75 

25.06 

71.64 

25.37 

71.53 

25.68 

76 

77 

72.80 

25.07 

72.69 

25.39 

72.58 

25.70 

72.47 

26.02 

77 

73 

73.75 

25.39 

73.64 

25.72 

73.53 

26.04 

73.41 

26.36 

78 

79 

74.70 

25.72 

74.58 

26.05 

74.47 

26.37 

74.35 

26.70 

79 

80 

75.64 

26.05 

75.53 

26.38 

75.41 

26.70 

75.29 

27.03 

80 

81 

76.59 

26.37 

76.47 

26.70 

76.35 

27.04 

76.24 

27.37 

81 

82 

77.53 

26.70 

77.42 

27.03 ' 

77.30 

27.37 

77.18 

27.71 

82 

83 

78.48 

27.02 

78.36 

27.36 

78.24 

27.71 

78.12 

28.05 

83 

84 

79.42 

27.35 

79.30 

27.69 

79.18 

28.04 

79.06 

28.39 

84 

85 

80.37 

27.67 

80.25 

28.02 

80.12 

28.37 

80.00 

28.72 

85 

86 

81.31 

28.00 

81.19 

28.35 

81.07 

28.71 

80.94 

29.06 

86 

37 

82.26 

28.32 

82.14 

28.68 

82.01 

29.04 

81.88 

29.40 

87 

88 

83.21 

28.65 

83.08 

29.01 

82.95 

29.37 

82.82 

29.74 

88 

89 

84.15 

28.98 

84.02 

29.34 

83.90 

29.71 

83.76 

30.07 

89 

90 

85.10 

29.30 

84.97 

29.67 

84.84 

30.04 

84.71 

30.41 

90 

91 

86.04 

29.63 

85.91 

30.00 

85.78 

30.38 

85.65 

30.75 

91 

92 

86.99 

29.95 

86.86 

30.33 

86.72 

30.71 

86.59 

31.09 

92 

93 

87.93 

30.28 

87.80 

30.66 

87.67 

31.04 

87.53 

31.43 

93 

94 

88.88 

30.60 

88.74 

30.99 

88.61 

31.38 

88.47 

31.76 

94 

95 

89.82 

30.93 

89.69 

31.32 

80.55 

31.71 

89.41 

32.10 

95 

96 

90.77 

31.25 

90.63 

31.65 

90.49 

32.05 

90.35 

32.44 

96 

97 

91.72 

31.58 

91.58 

31.98 

91.44 

32.38 

91.29 

32.78 

97 

98 

92.66 

31.91 

92.52 

32.31 

92.38 

32.71 

92.24 

33.12 

98 

99 

93.61 

32.23 

93.46 

32.64 

93.32 

33.05 

93.18 

33.45 

99 

100 

94.55 

32.56 

94.41 

32.97 

94.26 

33.38 

94.12 

33.79 

too 

© 

o 

Dep. J 

Lat. 

Dep. 

Lat. 

Dep* 

Lat. 

Dep. 

Lat. 

© 

o 

S3 

d 

+-> 

or> 

Q 

71 Deg. 

70} Deg. 

70} Deg. 

70} Deg. 

C$ 

m 

5 


F 






















































































42 


TRAVERSE TABLE. 


Distance. 

20 Deg. 

20$ Deg. 

1 

20^ Deg. 

201 Deg. 

Distance. 

Lat. 

Dep. 

Lat. 

Dep. | 

Lat. 

Dep. 

Lat. 

Dep. 

1 

0.94 

0.34 

0.94 

0.35 

0.94 

0.35 

0.94 

0.35 

1 

2 

1.88 

0.68 

1.88 

0.69 

1.87 

0.70 

1.87 

0.71 

2 

3 

2.82 

1.03 

2.84 

1.04 

2.81 

1.05 

2.81 

1.06 

3 

4 

3.76 

1.37 

3.75 

1.38 

3.75 

1.40 

3.74 

1.42 

4 

5 

4.70 

1.71 

4.69 

1.73 

4.68 

1.75 

4.68 

1.77 

5 

6 

5.64 

2.05 

5.63 

2.08 

5.62 

2.10 

5.61 

2.13 

6 

1 

6.58 

2.39 

6.57 

2.42 

6.56 

2.45 

6.55 

2.48 

7 

8 

7.52 

2.74 

7.51 

2.77 

7.49 

2.80 

7.48 

2.83 

8 

9 

8.46 

3.03 

8.44 

3.12 

8.43 

3.15 

8.42 

3.19 

9 

10 

9.40 

3.42 

• 

9.38 

3.46 

9.37 

3.50 

9.35 

3.54 

10 

11 

10.34 

3.76 

10.32 

3.81 

10.30 

3.85 

10.29 

3.90 

11 

12 

11.28 

4.10 

11.26 

4.15 

11.24 

4.20 

11.22 

4.25 

12 

13 

12.22 

4.45 

12.20 

4.50 

12.18 

4 • d5 

12.16 

4.61 

13 

14 

13.16 

4.79 

13.13 

4.85 

13.11 

4.90 

13.09 

4.96 

14 

15 

14.10 

5.13 

14.07 

5.19 

14.05 

5.25 

14.03 

5.31 

15 

16 

15.04 

5.47 

15.01 

5.54 

14.99 

5.60 

14.96 

5.67 

16 

17 

15.97 

5.81 

15.95 

5.88 

15.92 

5.95 

15.90 

6.02 

17 

18 

16.91 

6.16 

16.89 

6.23 

16.86 

6.30 

16.83 

6.38 

18 

19 

17.85 

6.50 

17.83 

6.58 

17.80 

6.65 

17.77 

6.73 

19 

20 

18.79 

6.84 

18.76 

6.92 

18.73 

7.00 

18.70 

7.09 

20 

21 

19.73 

7.18 

19.70 

7.27 

19.67 

7.35 

19.64 

7.44 

21 

22 

20.67 

7.52 

20.64 

7.61 

20.61 

7.70 

20.57 

7.79 

22 

23 

21.61 

7.87 

21.58 

7.96 

21.54 

8.05 

21.51 

8.15 

23 

24 

22.55 

8.21 

22.52 

8.31 

22.48 

8.40 

22.44 

8.50 

24 

25 

23.49 

8.55 

23.45 

8.65 

23.42 

8.76 

23.38 

8.86 

25 

26 

24.43 

8.89 

24.39 

9.00 

24.35 

9.11 

24.31 

9.21 

26 

27 

25.37 

9.23 

25.33 

9.35 

25.29 

9.46 

25.25 

9.57 

27 

28 

26.31 

9.58 

26.27 

9.69 

26.23 

9.81 

26.18 

9.92 

28 

29 

27.25 

9.92 

27.21 

10.04 

27.16 

10.16 

27.12 

10.27 

29 

30 

28.19 

10.26 

28.15 

10.38 

28.10 

10.51 

28.05 

10.63 

30 

31 

29.13 

10.60 

29.08 

10.73 

29.04 

10.86 

28.99 

10.98 

31 

32 

30.07 

10.94 

30.02 

11.08 

29.97 

11.21 

29.92 

11.34 

32 

33 

31.01 

11.29 

30.96 

11.42 

30.91 

11.56 

30.86 

11.69 

33 

34 

31.95 

11.63 

31.90 

11.77 

31.85 

11.91 

31.79 

12.05 

34 

35 

32.89 

11.97 

32.84 

12.11 

32.78 

12.26 

32.73 

12.40 

35 

36 

33.83 

12.31 

33.77 

12.46 

33.72 

12.61 

33.66 

12.75 

36 

37 

34.77 

12.65 

34.71 

12.81 

34.66 

12.96 

34.60 

13.11 

37 

38 

35.71 

13.00 

35.65 

13.15 

35.59 

13.31 

35.54 

13.46 

38 

39 

36.65 

13.34 

36.59 

13.50 

36.53 

13.66 

36.47 

13.82 

39 

40 

37.59 

13.68 

37.53 

13.84 

37.47 

14.01 

37.41 

14.17 

40 . 

41 

38.53 

14.02 

38.47 

14.19 

38.40 

14.36 

38.34 

14.53 

41 

42 

39.47 

14.36 

39.40 

14.54 

39.34 

14.71 

39.28 

14.88 

42 

43 

40.41 

14.71 

40.34 

14.88 

40.28 

15.06 

40.21 

15.23 

43 

44 

41.35 

15.05 

41.28 

15.23 

41.21 

15.41 

41.15 

15.59 

44 

45 

42.29 

15.39 

42.22 

15.58 

42.15 

15.76 

42.08 

15.94 

45 

46 

43.23 

15.73 

43.16 

15.92 

43.09 

16.11 

43.02 

16.30 

46 

47 

44.17 

16.07 

44.09 

16.27 

44.02 

16.46 

43.95 

16.65 

47 

48 

45.11 

16.42 

45.03 

16.61 

44.96 

16.81 

44.89 

17.01 

48 

49 

46.04 

16.76 

45.97 

16.96 

45.90 

17.16 

45.82 

17.36 

49 

50 

, r* •*> 

46.93 

17.10 

46.91 

17.31 

46.83 

17.51 

46.76 

17.71 

50 

| Distance. 

* 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Distance. 

70 Deg. 

. . ■ 

69$ Deg. 

694 Deg. 

. 

( 

69$ Deg. 







































































































TRAVERSE TABLE 


43 


F 

20 Deg. 

20i Deg. 

20^ Deg. 

20f Deg. 

d 

N« 

09 

S3 

3 

O 

<T> 

• 









r—- 

g 

o 

• 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

51 

47.92 

17.44 

47.85 

17.65 

47.77 

17.86 

47.69 

18.07 

51 

52 

48.86 

17.79 

48-79 

18.00 

48.71 

18.21 

48.63 

18.42 

52 

53 

49.80 

18.13 

49.72 

18.34 

49.64 

18.56 

49.56 

18.78 

53 

54 

50.74 

18.47 

50.66 

18.69 

50.58 

18.91 

50.50 

19.13 

54 

55 

51.68 

18.81 

51.60 

19.04 

51.52 

19.26 

51.43 

19.49 

55 

56 

52.62 

19.15 

52.54 

19.38 

52.45 

19.61 

52.37 

19.84 

56 

57 

53.56 

19.50 

53.48 

19.73 

53.39 

19.96 

53.30 

20.19 

57 

58 

54.50 

19.84 

54.42 

20.07 

54.33 

20.31 

54.24 

20.55 

58 

39 

55.44 

20.18 

55.35 

20.42 

55.26 

20.66 

55.17 

20.90 

59 

60 

56.38 

20.52 

56.29 

20.77 

56.20 

21.01 

56.11 

21.26 

60 

61 

57.32 

20.86 

57.23 

21.11 

57.14 

21.36 

57.04 

21.61 

61 

62 

58.26 

21.21 

58.17 

21.46 

58.07 

21.71 

57.98 

21.97 

62 

63 

59.20 

21.55 

59.11 

21.81 

59.01 

22.06 

58.91 

22.32 

63 

64 

60.14 

21.89 

60.04 

22.15 

59.95 

22.41 

59.85 

22.67 

64 

65 

61.08 

22.23 

60.93 

22.50 

60.88 

22.76 

60.78 

23.03 

65 

66 

62.02 

22.57 

61.92 

22.84 

61.82 

23.11 

61.72 

23.38 

66 

67 

62.96 

22.92 

62.86 

23.19 

62.76 

23.46 

62.65 

23.74 

67 

68 

63.90 

23.26 

63.80 

23.54 

63.69 

23.81 

63.59 

24.09 

68 

69 

64.84 

23.60 

64.74 

23.88 

64.63 

24.16 

64.52 

24.45 

69 

70 

65.78 

23.94 

65.67 

24.23 

65.57 

24.51 

65.46 

24.80 

70 

71 

66.72 

24.28 

66.61 

24.57 

66.50 

24.86 

66.39 

25.15 

71 

72 

67.66 

24.63 

67.55 

24 Qoy 

| 67.44 

25.21 

67.33 

25.51 

72 

73 

68.60 

24.97 

68.49 

25.27 

1 68.38 

25.57 

68.26 

25.86 

73 

74 

69.54 

25.31 

69.43 

25.61 

69.31 

25.92 

69.20 

26.22 

74 

75 

70.48 

25.65 

70.36 

25.96 

70.25 

26.27 

70.14 

26.57 

75 

76 

71.42 

25.99 

71.30 

26.30 

71.19 

26.62 

71.07 

26.93 

76 

! 77 

72.36 

26.34 

72.24 

26.65 

72.12 

26.97 

72.01 

27.28 

77 

78 

73.30 

26.68 

73.18 

27.00 

73.06 

27.32 

72.94 

27.63 

78 

79 

74.24 

27.02 

74.12 

27.34 

74.00 

27.67 

73.88 

27.99 

79 

80 

75.18 

27.36 

75.06 

27.69 

74.93 

28.02 

74.81 

28.34 

80 

81 

76.12 

27.70 

75.99 

28.04 

75.87 

28.37 

75.75 

28.70 

81 

82 

77.05 

28.05 

76.93 

28.38 

76.81 

28.72 

76.68 

29.05 

82 

ii 83 

77.99 

28.39 

77.87 

28.73 

77.74 

29.07 

77.62 

29.41 

83 

84 

78.93 

28.73 

78.81 

29.07 

78.68 

29.42 

78.55 

29.76 

84 

85 

79.87 

29.07 

79.75 

29.42 

79.62 

29.77 

79.49 

30.11 

85 

86 

80.81 

29.41 

80.68 

29.77 

80.55 

30.12 

80.42 

30.47 

86 

87 

81.75 

29.76 

81.62 

30.11 

81.49 

30.47 

81.36 

30.82 

87 

88 

82.69 

30.10 

82.56 

30.46 

82.43 

30.82 

82.29 

31.18 

88 

89 

83.63 

30.44 

83.50 

30.80 

83.36 

31.17 

83.23 

31.53 

89 

90 

84.57 

30.78 

84.44 

31.15 

84.30 

31.52 

84.16 

31.89 

90 | 

91 

85.51 

31.12 

85.38 

31.50 

85.24 

31.87 

85.10 

32.24 

91 

92 

86.45 

31.47 

86.31 

31.84 

86.17 

OQ 09 

86.03 

32.59 

92 

93 

87.39 

31.81 

87.25 

32.19 

87.11 

32.57 

86.97 

32.95 

93 

94 

88.33 

32.15 

88.19 

32.54 

88.05 

32.92 

87.90 

33.30 

94 

95 

89.27 

32.49 

89.13 

32.88 

88.98 

33.27 

88.84 

33.66 

95 

96 

90.21 

32.83 

90.07 

33.23 

89.92 

33.62 

89.77 

34.01 

96 

97 

91.15 

33.18 

91.00 

33.57 

90.86 

33.97 

90.71 

34.37 

97 

! 98 

92.09 

33.52 

91.94 

33.92 

91.79 

34.32 

91.64 

34.72 

98 

[ 99 

93-03 

33.86 

92.88 

34.27 

92.73 

34.67 

92.58 

35.07 

99 

100 

93-97 

34.20 

93.82 

34-61 

| 93.67 

35.02 

93.51 

35.43 

100 

6 

c 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

<V 

V 

q 

c 

■*.> 

: Q 

70 Deg. 

i 

69$ Deg. 

- „——z; 

1 r 

69i Deg. 

i 

69$ Deg. 

ct5 

00 

Q 
























































































44 


TRAVERSE TABLE 


| Distance. 

21 Deg. 

2H Deg. 

21J Deg. 

211 Deg. 

IrT- 

i Distance. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

1 

0.93 

0.36 

0.93 

0.36 

0.93 

0.37 

0.93 

0.37 

1 

2 

1.87 

0.72 

1.86 

0.72 

1.86 

0.73 

1.86 

0.74 

2 

3 

2.80 

1.08 

2.80 

1.09 

2.79 

1.10 

2.79 

1.11 

3 

4 

3.73 

1.43 

3.73 

1.45 

3.72 

1.47 

3.72 

1.48 

4 

5 

4.67 

1.79 

4.66 

1.81 

4.65 

1.83 

4.64 

1.85 

5 

6 

5.60 

2.15 

5.59 

2.17 

5.58 

2.20 

5.57 

2.22 

6 

7 

6.54 

2.51 

6.52 

2.54 

6.51 

2.57 

6.50 

2.59 

nr 

( 

8 

7.47 

2.87 

7.46 

2.90 

7.44 

2.93 

7.43 

2.96 

8 

9 

8.40 

3.23 

8.39 

3.26 

8.37 

3.30 

8.36 

3.34 

9 

10 

9.34 

3.58 

9.32 

3.62 

9.30 

3.67 

9.29 

3.71 

10 

11 

10.27 

3.94 

10.25 

3.99 

10.23 

4.03 

10.22 

4.08 

11 ! 

12 

11.20 

4.30 

11.18 

4.35 

11.17 

4.40 

11.15 

4.45 

12 

13 

12.14 

4.66 

12.12 

4.71 

12.10 

4.76 

12.07 

4.82 

13 

14 

13.07 

5.02 

13.05 

5.07 

13.03 

5.13 

13.00 

5.19 

14 

15 

14.00 

5.38 

13.98 

5.44 

13.96 

5.50 

13.93 

5.56 

15 

16 

14.94 

5.73 

14.91 

5.80 

14.89 

5.86 

14.86 

5.93 

16 

17 

15.87 

6.09 

15.84 

6.16 

15.82 

6.23 

15.79 

6.30 

17 

18 

16.80 

6.45 

16.78 

6.52 

16.75 

6.60 

16.72 

6.67 

18 

19 

17.74 

6.81 

17.71 

6.89 

17.68 

6.96 

17.65 

7.04 

19 

20 

18.67 

7.17 

18.64 

7.25 

18.61 

7.33 

18.58 

7.41 

20 

21 

19.61 

7.53 

19.57 

7.61 j 

19.54 

7.70 

19.50 

7.78 

21 

22 

20.54 

7.88 

20.50 

7.97 

20.47 

8.06 

20.43 

8.15 

22 

23 

21.47 

8.24 

21.44 

8.34 

21.40 

8.43 

21.36 

8.52 

23 

24 

22.41 

8.60 

22.37 

8.70 

22.33 

8.80 

22.29 

8.89 

24 

25 

23.34 

8.96 

23.30 

9.06 

23.26 

9.16 

23.22 

9.26 

25 

26 

24.27 

9.32 

24.23 

9.42 

24.19 

9.53 

24.15 

9.63 

26 

27 

25.21 

9.68 

25.16 

9.79 

25.12 

9.90 

25.08 

10.01 

27 

28 

26.14 

10.03 

26.10 

10.15 

26.05 

10.26 

26.01 

10.38 

28 

29 

27.07 

10.39 

27.03 

10.51 

26.98 

10.63 

26.94 

10.75 

29 

30 

28.01 

10.75 

27.96 

10-87 

27.91 

11.00 

27.86 

11.12 

30 

31 

28.94 

11.11 

28.89 

11.24 

28.84 

11.36 

28.79 

11.49 

31 

32 

29.87 

11.47 

29.82 

11.60 

29.77 

11.73 

29.72 

11.86 

32 

33 

30.81 

11.83 

30.76 

11.96 

30.70 

12.09 

30.65 

12.23 

33 

34 

31.74 

12.18 

31.69 

12.32 

31.63 

12.46 

31.58 

12.60 

34 

35 

32.68 

12.54 

32.62 

12.69 

32.56 

12.83 

32.51 

12.97 

35 

36 

33.61 

12.90 

33.55 

13.05 

33.50 

13.19 

33.44 

13.34 

36 

37 

34.54 

13.26 

34.48 

13.41 

34.43 

13.56 

34.37 

13.71 

37 

38 

35.48 

13.62 

35.42 

13.77 

35.36 

13.93 

35.29 

14.08 

38 

39 

36.41 

13.98 

36.35 

14.14 

36.29 

14.29 

36.22 

14.45 

39 

40 

37.34 

14.33 

37.28 

14.50 

37.22 

14.66 

37.15 

14.82 

40 

41 

38.28 

14.69 

38.21 

14.86 

38.15 

15.03 

38.08 

15.19 

41 

42 

39.21 

15.05 

39.14 

15.22 

39.08 

15.39 

39.01 

15.56 

42 

43 

40.14 

15.>11 

40.08 

15.58 

40.01 

15.76 

39.94 

15.93 

43 

44 

41.08 

15.77 

41.01 

15.95 

40.94 

16.13 

40.87 

16.30 

44 

45 

42.01 

16.13 

41.94 

16.31 

41.87 

16.49 

41.80 

16.68 

45 

46 

42.94 

16.48 

42.87 

16.67 

42.80 

16.86 

42.73 

17.05 

46 

47 

43.88 

16.84 

43.80 

17.03 

43.73 

17.23 

43.65 

17 42 

47 

48 

44.81 

17.20 

44.74 

17.40 

44.66 

17.59 

44.58 

17.79 

48 

49 

45.75 

17.56 

45.67 

17.76 

45.59 

17.96 

45.51 

18.16 

49 

50 

46.68 

17.92 

46.60 

18.12 

i 

46.52 

18.33 

46.44 

18.53 

50 

Distance. 

1 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

CLf 

O 

S3 

CTJ k 

CO 

• «-M 

Q 

69 Deg. 

63| Deg. 

68J Deg. 

68£ Deg. 








































































45 


TRAVERSE TABLE. 


| Distance. 

21 Deg. 

2H Deg. 

21£ Deg. 

21| Deg. 

Distance. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

51 

47.61 

18.28 

47.53 

18.48 

47.45 

18.69 

47.37 

18.90 

51 

52 

48.55 

18.64 

48.46 

18.85 

48.38 

19.06 

48.30 

19.27 

52 

53 

49.48 

18.99 

49.40 

19.21 

49.31 

19.42 

49.23 

19.64 

53 

54 

50.41 

19.35 

50.33 

19.57 

50.24 

19.79 

50.16 

20.01 

54 

55 

51.35 

19.71 

51.26 

19.93 

51.17 

20.16 

51.08 

20.38 

55 

56 

52.28 

20.07 

52.19 

20.30 

52.10 

20.52 

52.01 

20.75 

56 

57 

53.21 

20.43 

53.12 

20.66 

53.03 

20.89 

52.94 

21.12 

57 

53 

54.15 

20.79 

54.06 

21.02 

53.96 

21.26 

53.87 

21.49 

58 

59 

55.08 

21.14 

54.99 

21.38 

54.89 

21.62 

54.80 

21.86 

59 

60 

56.01 

21.50 

55.92 

21.75 

55.83 

21.99 

55.73 

22.23 

60 

61 

56.95 

21.86 

56.85 

22.11 

56.76 

22.36 

56.66 

22.60 

61 

62 

57.88 

22 22 

57.78 

22.47 

57.69 

22.72 

57.59 

22.97 

62 

63 

58.82 

22.58 

58.72 

22.83 

58.62 

23.09 

58.52 

23.35 

63 

64 

59.75 

22.94 

59.65 

23.20 

59.55 

23.46 

59.44 

23.72 

64 

65 

60.63 

23.29 

60.58 

23.56 

60.48 

23.82 

60.37 

24.09 

65 

66 

61.62 

23.65 

61.51 

23.92 

61.41 

24.19 

61.30 

24.46 

66 

67 

62.55 

24.01 

62.44 

24.28 

62.34 

24.56 

62.23 

24.83 

67 

63 

63.48 

24.37 

63.38 

24.65 

63.27 

24.92 

63.16 

25.20 

68 

69 

64.42 

24.73 

64.31 

25.01 

64.20 

25.29 

64.09 

25.57 

69 

70 

65.35 

25.09 

65.24 

25.37 

65.13 

25.66 

65.02 

25.94 

70 

71 

66.23 

25.44 

66.17 

25.73 

66.06 

26.02 

65.95 

26.31 

71 

72 

67.22 

25.80 

67.10 

26.10 

66.99 

26.39 

66.87 

26.68 

72 

73 

68.15 

26.16 

68.04 

26.46 

67.92 

26.75 

67.80 

27.05 

73 

74 

69.08 

26.52 

68.97 

26.82 

68.85 

27.12 

68.73 

27>. 42 

74 

75 

70.02 

26.88 

69.90 

27.18 

69.78 

27.49 

69.66 

27.79 

75 

76 

70.95 

27.24 

70.83 

27.55 

70.71 

27.85 

70.59 

28.16 

76 

77 

71.89 

27.59 

71.76 

27.91 

71.64 

28.22 

71.52 

28.53 

77 

73 

72.82 

27.95 

72.70 

28.27 

72.57 

28.59 

72.45 

28.90 

78 

79 

73.75 

28.31 

73.63 

28.63 

73.50 

28.95 

73.38 

29.27 

79 

30 

74.69 

28.67 

74.56 

29.00 

74.43 

29.32 

74.30 

29.64 

80 

81 

75.62 

29.03 

75.49 

29.36 

75.36 

29.69 

75.23 

30.02 

81 

82 

76.55 

29.39 

76.42 

29.72 

76.29 

30.05 

76.16 

30.39 

82 

33 

77.49 

29.74 

77.36 

30.08 

77.22 

30.42 

77.09 

30.76 

83 

84 

78.42 

30.10 

78.29 

30.44 

78.16 

30.79 

78.02 

31.13 

84 

85 

79.35 

30.46 

79.22 

30.81 

79.09 

31.15 

78.95 

31.50 

85 

86 

80.29 

30.82 

80.15 

31.17 

80.02 

31.52 

79.88 

31.87 

86 

87 

81.22 

31.18 

81.08 

31.53 

80.95 

31.89 

80.81 

32.24 

87 

88 

82.16 

31.54 

82.02 

31.89 

81,88 

32.25 

81.74 

32.61 

88 

89 

83.09 

31.89 

82.95 

32.26 

82.81 

32.62 

82.66 

32.98 

89 

90 

84.02 

32.25 

83.88 

32.62 

83.74 

32.99 

83.59 

33.35 

90 

91 

84.96 

32.61 

84.81 

32.98 

84.67 

33.35 

84.52 

33.72 

91 

92 

85.89 

32.97 

85.74 

33.34 

85.60 

33.72 

85.45 

34.09 

92 

93 

86.82 

33.33 

86.68 

33.71 

86.53 

34.08 

86.38 

34.46 

93 

94 

87.76 

33.69 

87.61 

34.07 

87.46 

34.45 

87.31 

34.83 

94 

95 

88.69 

34.04 

88.54 

34.43 

88.39 

34.82 

88.24 

35.20 

95 

96 

89.62 

34.40 

89.47 

34.79 

89.32 

35.18 

89.17 

35.57 

96 

97 

90.56 

34.76 

90.40 

35.16 

90.25 

35.55 

90.09 

35.94 

97 

98 

91.49 

35.12 

91.34 

35.52 

91.18 

35.92 

91.02 

36.31 

98 

99 

92.42 

35.48 

92.27 

35.88 

92.11 

36.28 

91.95 

36.69 

99 

100 

93.36 

35.84 

93.20 

36.24 

93.04 

36.65 

92.88 

37.06 

100 

6 

V 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

<D 

O 

CJ 

ci 

-*-> 

Ui 
• H 

a ; 

69 Deg. 

68f Deg. 

684 Deg. 

684 Deg. 

05 

U) 

• H 

Q 


















































































40 


TRAVERSE TABLE 


0 

U0* 

r-t- 

» 

22 Deg. 

22} Deg. 

22} Deg. 

22} Deg. 

5 

<-*■ 

3 

o 

(T> 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

n 

n 

• 

1 

0.93 

0.37 

0.93 

0.38 

0.92 

0.38 

0.92 

0.39 

1 

2 

1.85 

0.75 

1.85 

0.76 

1.85 

0.77 

1.84 

0.77 

2 

3 

2.73 

1.12 

2.78 

1.14 

2.77 

1.15 

2.77 

1.16 

3 

4 

3.71 

1.50 

3.70 

1.51 

3.70 

1.53 

3,69 

1.55 

4 

5 

4.64 

1.87 

4.63 

1.89 

4.62 

1.91 

4.61 

1.93 

5 

6 

5.56 

2.25 

5.55 

2.27 

5.54 

2.30 

5.53 

2.32 

6 

7 

6.49 

2.62 

6.48 

2.65 

6.47 

2.68 

6.46 

2.71 

7 

8 

7.42 

3.00 

7.40 

3.03 

7.39 

3.06 

7.38 

3.09 

8 

9 

8.34 

3.37 

8.33 

3.41 

8.31 

3.44 

8.30 

3.48 

9 

10 

9.27 

3.75 

9.26 

3.79 

9.24 

3.83 

9.22 

3.87 

10 

11 

10.20 

4.12 

10.18 

4.17 

10.16 

4.21 

10.14 

4.25 

11 

12 

11.13 

4.50 

11.11 

4.54 

11.09 

4.59 

11.07 

4.64 

12 

13 

12.05 

4.87 

12.03 

4.92 

12.01 

4.97 

11.99 

5.03 

13 

14 

12.98 

5.24 

12.96 

5.30 

12.93 

5.36 

12.91 

5.41 

14 

15 

13.91 

5.62 

13.88 

5.68 

13.86 

5.74 

13.83 

5.80 

15 

16 

14.83 

5.99 

14.81 

6.06 

14.78 

6.12 

14.76 

6.19 

16 

17 

15.76 

6.37 

15.73 

6.44 

15.71 

6.51 

15.68 

6.57 

17 

18 

16.69 

6.74 

16.66 

6.82 

16.63 

6.89 

16.60 

6.96 

18 

19 

17.62 

7.12 

17.59 

7.19 

17.55 

7.27 

17.52 

7.35 

19 

20 

18.54 

7.49 

18.51 

7.57 

18.48 

7.65 

18.44 

7.73 

20 

21 

19.47 

7.87 

19.44 

7.95 

19.40 

8.04 

19.37 

8.12 

21 

22 

20.40 

8.24 

20.36 

8.33 

20.33 

8.42 

20.29 

8.51 

22 

23 

21.33 

8.62 

21.29 

8.71 

21.25 

8.80 

21.21 

8.89 

23 

24 

22.25 

8.99 

22.21 

9.09 

22.17 

9.18 

22.13 

9.28 

24 

,25 

23.18 

9.37 

23.14 

9.47 

23.10 

9.57 

23.05 

9.67 

25 

26 

24.11 

9.74 

24.06 

9.84 

24.02 

9.95 

23.98 

10.05 

26 

27 

25.03 

10.11 

24.99 

10.22 

24.94 

10.33 

24.90 

10-44 

27 

28 

25.96 

10.49 

25.92 

10.60 

25.87 

10.72 

25.82 

10.83 

28 

29 

26.89 

10.86 

26.84 

10.98 

26.79 

11.10 

26.74 

11.21 

29 

30 

27.82 

11.24 

27.77 

11.36 

27.72 

11.48 

27.67 

11.60 

30 

31 

28.74 

11.61 

28.69 

11.74 

28.64 

11.86 

28.59 

11.99 

31 

32 

29.67 

11.99 

29.62 

12.12 

29.56 

12.25 

29.51 

12.37 

32 

33 

30.60 

12.36 

30.54 

12,50 

30.49 

12.63 

30.43 

12.76 

33 

34 

31.52 

12.74 

31.47 

12.87 

31.41 

13.01 

31.35 

13.15 

34 

35 

32.45 

13.11 

32.39 

13.25 

32.34 

13.39 

32.28 

13.53 

35 

36 

33.38 

13.49 

33.32 

13.63 

33.26 

13.78 

33.20 

13.92 

36 

37 

34.31 

13.86 

34.24 

14.01 

34.18 

14.16 

34.12 

14.31 

37 

38 

35.23 

14.24 

35.17 

14.39 

35.11 

14.54 

35.04 

14.70 

38 

39 

36.16 

14.61 

36.10 

14.77 

36.03 

14.92 

35.97 

15.08 

39 

40 

37.09 

14.98 

37.02 

15.15 

36.96 

15.31 

36.89 

15.47 

40 

41 

38.01 

15.36 

37.95 

15.52 

37.88 

15.69 

37.81 

15.86 

41 

42 

38.94 

15.73 

38.87 

15.90 

38.80 

16.07 

38.73 

16.24 

42 

43 

39.87 

16.11 

39.80 

16.28 

39.73 

16.46 

39.65 

16.63 

43 

44 

40.80 

16.48 

40.72 

16.66 

40.65 

16.84 

40.58 

17.02 

44 

45 

41.72 

16.86 

41.65 

17.04 

41.57 

17.22 

41.50 

17.40 

45 

46 

42.65 

17.23 

42.57 

17.42 

42.50 

17.60 

42.42 

17.79 

46 

47 

43.58 

17.61 

43.50 

17.80 

43.42 

17.99 

43.34 

18.18 

47 

48 

44.50 

17.98 

44.43 

18.18 

44.35 

18.37 

44.27 

18.56 

48 

49 

45.43 

18.36 

45.35 

18.55 

45.27 

18.75 

45.19 

18.95 

49 

50 

46.36 

18.73 

46.28 

18.93 

46.19 

19.13 

46.11 

19.34 

50 

« 

o 

fl 

Dep. 1 

Lat. 

Dep. 

Lat. 

Dep. J 

Lat. 

Dep. 

Lat. 

a; 

o 

Sf) 

* r~i 

Q 

68 Deg. 

67| Deg. 

67} Deg. 

67} Deg. 

ct 

Vi 
• — i 

2 














































































traverse Table 


47 


o 

rn 

P 

22 Deg. 

I 

22:1 Deg. 

22£ Deg. 

22| Deg. 

tJ 
>—. 
rjo 
c-*- 

P 

l 5 

'? 

L at. 

Dep. 

| Lat. 

Dep. 

Lat. 

I Dep. 

Lat. 

Dep. 

E3 

O 

m 

• 

51 

47.29 

19.10 

47.20 

19.31 

47.12 

19.52 

47.03 

19.72 

51 

52 

48.21 

19.48 

48.13 

19.69 

48.04 

19.90 

47.95 

20.11 

52 

53 

49.14 

19.85 

49.05 

20.07 

48.97 

20.28 

48.88 

20.50 

53 

54 

50.07 

20.23 

49.98 

20.45 

49.89 

20.66 

49.80 

20.88 

54 

55 

51.00 

20.60 

50.90 

20.83 

50.81 

21.05 

50.72 

21.27 

55 

56 

51.92 

20.98 

51.83 

21*20 

51.74 

21.43 

51.64 

21.66 

56 

57 

52.85 

21.35 

52.76 

21.58 

52.66 

21.81 

52.57 

22.04 

57 

53 

53.78 

21.73 

53.68 

21.96 

53.59 

22.20 

53.49 

22.43 

58 

59 

54.70 

22.10 

54.61 

22.34 

54.51 

22.58 

54.41 

22.82 

59 

60 

55.63 

22.48 

55.53 

22.72 

55.43 

22.96 

55.33 

23.20 

60 

61 

56.56 

22.85 

56.47 

23.10 

56.36 

23.34 

56.25 

23.59 

61 

62 

57.49 

23.23 

57.38 

23.48 

57.28 

23.73 

57.18 

23.98 

62 

63 

58.41 

23.60 

58.31 

23.85 

58.20 

24.11 

58.10 

24.36 

63 

64 

59.34 

23.97 

59.23 

24.23 

59.13 

24.49 

59.02 

24.75 

64 

65 

60.27 

24.35 

60.16 

24.61 

60.05 

24.87 

59.94 

25.14 

65 

66 

61.19 

24.72 

61.09 

24.99 

60.98 

25.26 

60.87 

25.52 

66 

\ 67 

62.12 

25.10 

62.01 

25.37 

61.90 

25.64 

61.79 

25.91 

67 

68 

63.05 

25.47 

62.94 

25.75 

62.82 

26.02 

62.71 

26.30 

68 

69 

63.98 

25.85 

63.86 

26.13 

63.75 

26.41 

63.63 

26.68 

69 

70 

64.90 

26.22 

64.79 

26.51 

64.67 

26.79 

64.55 

27.07 

70 

71 

65 • 83 

26.60 

65.71 

26.88 

65.60 

27.17 

65.48 

27.46 

71 

72 

66.76 

26.97 

66.64 

27.26 

66.52 

27.55 

66.40 

27.84 

72 

73 

67.68 

27.35 

67.56 

27.64 

67.44 

27.94 

67.32 

28.23 

73 

74 

68.61 

27.72 

68.49 

28.02 

68.37 

28.32 

68.24 

28.62 

74 

75 

69 54 

28.10 

69.42 

28.40 

69.29 

28.70 

69.17 

29.00 

75 

76 

70.47 

28.47 

70.34 

28.78 

70.21 

29.08 

70.09 

29.39 

76 

77 

71.39 

23.84 

71.27 

29.16 

! 71.14 

29.47 

71.01 

29.78 

77 

78 

72.32 

29.22 

72.19 

29.53 

72.06 

29.85 

71.93 

30.16 

78 

79 

73.25 

29.59 

73.12 

29.91 

72.99 

30.23 

72.85 

30.55 

79 

80 

74.17 

29.97 

74.04 

30.29 

73.91 

30.61 

73.78 

30.94 

80 

81 

75.10 

30.34 

74.97 

30.67 

74.83 

31.00 

74.70 

31.32 

81 

82 

76.03 

30.72 

75.89 

31.05 

75.76 

31.38 

75.62 

31.71 

82 

83 

76.96 

31.09 

76.82 

31.43 

76.68 

31.76 

76.54 

32.10 

83 

84 

77.88 

31.47 

77.75 

31.81 

77.61 

32.15 

77.46 

32.48 

84 

85 

78.81 

31.84 

78.67 

32.19 

78.53 

32,53 

78.39 

32.87 

85 

86 

79.74 

32.22 

79.60 

32.56 

79.45 

32.91 

79.31 

33.26 

86 

87 

80.66 

32.59 

80.52 

32.94 

80*38 

33.29 

80.23 

33.64 

87 

88 

81.59 

32.97 

81.45 

33.32 

81.30 

33.68 

81.15 

34.03 

88 

89 

82.52 

33.34 

82.37 

33.70 

82.23 

34.06 

82.08 

34.42 

89 

90 

83.45 

33.71 

83.30 

34.08 

83.15 

34.44 

83.00 

34.80 

90 

91 

84.37 

34.09 

84.22 

34.46 1 

84.07 

34.82 

83.92 

35.19 

91 

92 

85.30 

34.46 

85.15 

34.84 

85.00 

35.21 1 

84.84 

35.58 

92 

93 

86.23 

34.84 

86.08 

35.21 

85.92 

35.59 

85.76 

35.96 

93 

94 

87.16 

35.21 

87.00 

35.59 

86.84 

35.97 

86.69 

36.35 

94 

95 

88.03 

35.59 

87.93 

35.97 

87.77 

36.35 

87.61 

36.74 

95 

96 

89.01 

35.96 

88.85 

36.35 

88.69 

36.74 

88.53 

37.12 

96 

97 

89.94 

36.34 

89.78 

36.73 

89.62 

37.12 

89.45 

37.51 

97 

98 

90.86 

36.71 

90.70 

37.11 

90.54 

37.50 

90.38 

37.90 

98 

99 

91.79 

37.09 

91.63 

37.49 

91.46 

37.89 

91.30 

38.28 

99 

100 

92.72 

37.46 

92.55 

37.86 

92.39 

38.27 

92.22 

38.67 

100 

© 

o 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. j 

Lat. 

Dep. 

Lat. 

• 

© 

o 

a 

Cl 

VI 

• •»< 

Q 

68 Deg. 

67$ Deg. 

67$ Deg. 

67$ Deg. 

d 

•+-» 

VJ 
• H 

Q 

— J 




































































































TRAVERSE TABLE 



Distance. 

23 Deg. 

23J Deg. 

j 

23£ Deg. | 

23| Deg. 

Distance. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

1 

0.92 

0.39 

0.92 

0.39 

0.92 

0.40 

0.92 

0.40 

1 

2 

1.84 

0.78 

1.84 

0.79 

1.83 

0.80 

1.83 

0.81 

2 

3 

2.76 

1.17 

2.76 

1.18 

2.75 

1.20 

2.75 

1.21 

3 

4 

3.68 

1.56 

3.68 

1.58 

3.67 

1.59 

3.66 

1.61 

4 

5 

4.60 

1.95 

4.59 

1.97 

4.59 

1.99 

4.58 

2.01 

5 

6 

5.52 

2.34 

5.51 

2.37 

5.50 

2.39 

5.49 

2.42 

6" 

7 

6.44 

2.74 

6.43 

2.76 

6.42 

2.79 

6.41 

2.82 

7 

8 

7.36 

3.13 

7.35 

3.16 

7.34 

3.19 

7.32 

3.22 

8 

9 

8.28 

3.52 

8.27 

3.55 

8.25 

3.59 

8.24 

3.62 

9 

10 

9.20 

3.91 

9.19 

3.95 

9.17 

3.99 

9.15 

4.03 

10 

11 

10.13 

4.30 

10.11 

4.34 

10.09 

4.39 

10.07 

4.43 

11 

12 

11.05 

4.69 

11.03 

4.74 

11.00 

4.78 

10.98 

4.83 

12 

13 

11.97 

5.08 

11.94 

5.13 

11.92 

5.18 

11.90 

5.24 

13 

14 

12.89 

5.47 

12.86 

5.53 

12.84 

5.58 

12.81 

5.64 

14 

15 

13.81 

5.86 

13.78 

5.92 

13.76 

5.98 

13.73 

6.04 

15 

16 

14.73 

6.25 

14.70 

6.32 

14.67 

6.38 

14.64 

6.44 

16 

17 

15.65 

6.64 

15.62 

6.71 

15.59 

6.78 

15.56 

6.85 

17 

18 

16.57 

7.03 

16.54 

7.11 

16.51 

7.18 

16.48 

7.25 

18 

19 

17.49 

7.42 

17.46 

7.50 

17.42 

7.58 

17.39 

7.65 

19 

20 

18.41 

7.81 

18.38 

7.89 

18.34 

7.97 

18.31 

8.05 

20 

21 

19.33 

8.21 

19.29 

8.29 

19.26 

8.37 

19.22 

8.46 

21 

22 

20.25 

8.60 

20.21 

8.68 

20.18 

8.77 

20.14 

8.86 

22 

23 

21.17 

8.99 

21.13 

9.08 

21.09 

9.17 

21.05 

9.26 

23 

24 

22.09 

9.38 

22.05 

9.47 

22.01 

9.57 

21.97 

9.67 

24 . 

25 

23.01 

9.77 

22.97 

9.87 

22.93 

9.97 

22.88 

10.07 

25 

26 

23.93 

10.16 

23.89 

10.26 

23.84 

10.37 

23.80 

10.47 

26 

27 

24.85 

10.55 

24.81 

10.66 

24.76 

10.77 

24.71 

10.87 

27 

28 

25.77 

10.94 

25.73 

11.05 

25.68 

11.16 

25.63 

11.28 

28 

29 

26.69 

11.33 

26.64 

11.45 

26.59 

11.56 

26.54 

11.68 

29 

30 

27.62 

11.72 

27.56 

11.84 

27.51 

11.96 

27.46 

12.08 

30 

31 

28.54 

12.11 

28.48 

12.24 

28.43 

12.36 

28.37 

12.49 

31 

32 

29.46 ' 

12.50 

29.40 

12.63 

29.35 

12.76 

29.29 

12.89 

32 

33 

30.38 

12.89 

30.32 

13.03 

30.26 

13.16 

30.21 

13.29 

33 

34 

31.30 

13.28 

31.24 

13.42 

31.18 

13.56 

31.12 

13.69 

34 

35 

32.22 

13.68 

32.16 

13.82 

32.10 

13.96 

32.04 

14.10 

35 

36 

33.14 

14.07 

33.08 

14.21 

33.01 

14.35 

32.95 

14.50 

36 

37 

34.06 

14.46 

34.00 

14.61 

33.93 

14.75 

33.87 

14.90 

37 

38 

34.98 

14.85 

34.91 

15.00 

34.85 

15.15 

34.78 

15.30 

38 

39 

35.90 

15.24 

35.83 

15.39 

35.77 

'15.55 

35.70 

15.71 

39 

40 

36.82 

15.63 

36.75 

15.79 

36.68 

15.95 

36.61 

16.11 

40 

41 

37; 74 

16.02 

37.67 

16.18 

37.60 

16.35 

37.53 

16.51 

41 

42 

38.66 

16.41 

38.59 

16.58 

38.52 

16.75 

38.44 

16.92 

42 

43 

39.58 

16.80 

39.51 

16.97 

39.43 

17.15 

39.36 

17.32 

43 

44 

40.50 

17.19 

40.43 

17.37 

40.35 

17.54 

40.27 

17.72 

44 

45 

41.42 

17.58 

41.35 

17.76 

41.27 

17.94 

41.19 

18.12 

45 

46 

42.34 

17.97 

42.26 

18.16 

42.18 

18.34 

42.10 

18.53 

46 

47 

43.26 

18.36 

43.18 

18.55 

43.10 

18.74 

43.02 

18.93 

47 

48 

44.18 

18.76 

44.10 

18.95 

44.02 

19.14 

43.93 

19.33 

48 

49 

45.10 

19.15 

45.02 

19.34 

44.94 

19.54 

44.85 

19.73 

49 

50 

46.03 

19.54 

45.94 

19.74 

45.85 

19.94 

45.77 

20.14 

50 

Distance. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Distance. 

67 Deg. 

i » 

66f Deg. 

66£ Deg. 

66^ Deg. 










































































TRAVERSE TABLE 


49 


o 

(n‘ 

r-t- 

95 

! 

1 23 Deg. 

23i 

Deg. 

23£ 

Deg. 

23f 

Deg. 

0 

ffi* 

E 

o 

(6 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

3 

o 

(t> 

51 

46.95 

19.93 

46.86 

20.13 

46.77 

20.34 

46.68 

20.54 

51 

52 

47.87 

20.32 

47.73 

20.53 

47.69 

20.73 

47.60 

20.94 

52 

53 

48.79 

20.71 

48.70 

20.92 

48.60 

21.13 

48.51 

21.35 

53 

i 54 

49.71 

21.10 

49.61 

21.32 

49.52 

21.53 

49.43 

21.75 

54 

55 

50.63 

21.49 

50.53 

21.71 

50.44 

21.93 

50.34 

22.15 

55 

; 56 

51.55 

21.88 

51.45 

22.11 

51.36 

22.33 

51.26 

22.55 

56 

57 

52.47 

22.27 

52.37 

22.50 

52.27 

22.73 

52.17 

22.96 

57 

58 

53.39 

22.66 

53.29 

22.90 

53.19 

23.13 

53.09 

23.36 

58 

! 59 

54.31 

23.05 

54.21 

23.29 

54.11 

23.53 

54.00 

23.76 

59 

GO 

55.23 

23.44 

55.13 

23.68 

55.02 

23.92 

54.92 

24.16 

60 

61 

56.15 

23.83 

56.05 

24.08 

55.94 

24.32 

55.83 

24.57 

61 

62 

57.07 

24.23 

56.97 

24.47 

56.86 

24.72 

56.75 

24.97 

62 

63 

57.99 

24.62 

57.88 

24.87 

57.77 

25.12 

57.66 

25.37 

63 

64 

58.91 

25.01 

58.80 

25.26 

58.69 

25.52 

58.58 

25.78 

64 

65 

59.83 

25.40 

59.72 

25.66 

59.61 

25.92 

59.50 

26.18 

65 

66 

60.75 

25.79 

60.64 

26.05 

60.53 

26.32 

60.41 

26.58 

66 

67 

61.67 

26.18 

61.56 

26.45 

61.44 

26.72 

61.33 

26.98 

67 

68 

62.59 

26.57 

62.48 

26.84 

62.36 

27.11 

62.24 

27.39 

68 

69 

63.51 

26.96 

63.40 

27.24 

63.28 

27.51 

63.16 

27.79 

69 

70 

64.44 

27.35 

64.32 

27.63 

64.19 

27.91 

64.07 

28.19 

70 

71 

65.36 

27.74 

65.23 

28.03 

65.11 

28.31 

64.99 

28.59 

71 

72 

66.28 

28.13 

66.15 

28.42 

66.03 

28.71 

65.90 

29.00 

72 

73 

67.20 

28.52 

67.07 

28.82 

66.95 

29.11 

66.82 

29.40 

73 

74 

68.12 

28.91 

67.99 

29.21 

67.86 

29.51 

67.73 

29.80 

74 

75 

69.04 

29.30 

68.91 

29.61 

68.78 

29.91 

68.65 

30.21 

75 

76 

69.96 

29.70 

69.83 

30.00 

69.70 

30.30 

69.56 

30.61 

76 

77 

70.88 

30.09 

70.75 

30.40 

70.61 

30.70 

70.48 

31.01 

77 

78 

71.80 

30.48 

71.67 

30.79 

71.53 

31.10 

71.39 

31.41 

78 

79 

72.72 

30.87 

72.58 

31.18 

72.45 

31.50 

72.31 

31.82 

79 

80 

73.64 

31.26 

73.50 

31.58 

73.36 

31.90 

73.22 

32.22 

80 

81 

74.56 

31.65 

74.42 

31.97 

74.28 

32.30 

74.14 

32.62 

81 

82 

75.48 

32.04 

75.34 

32.37 

75.20 

32.70 

75.06 

33.03 

82 

83 

76.40 

32.43 

76.26 

32.76 

76.12 

33.10 

75.97 

33.43 

83 

84 

77.32 

32.82 

77.18 

33.16 

77.03 

33.49 

76.89 

33.83 

84 

85 

78.24 

33.21 

78.10 

33.55 

77.95 

33.89 

77.80 

34.23 

85 

86 

79.16 

33.60 

79.02 

33.95 

78.87 

34.29 

78.72 

34.64 

86 

87 

80.08 

33.99 

79.93 

34.34 

79.78 

34.69 

79.63 

35.04 

87 

88 

81.00 

34.38 

80.85 

34.74 

80.70 

35.09 

80.55 

35.44 

88 

89 

81.92 

34.78 

81.77 

35.13 

81.62 

35.49 

81.46 

35.84 

89 

90 

82.85 

35.17 

82.69 

35.53 

82.54 

35.89 

82.38 

36.25 

90 

91 

83.77 

35.56 

83.61 

35.92 

83.45 

36.29 

83.29 

36.65 

91 

92 

84.69 

35.95 

84.53 

36.32 

84.37 

36.68 1 

84.21 

37.05 

92 

93 

85.61 

36.34 

85.45 

36.71 

85.29 

37.08 

85.12 

37.46 

93 

94 

86.53 

36.73 

86.37 

37.11 

86.20 

37.48 

86.04 

37.86 

94 

95 

87.45 

37.12 

87.29 

37.50 

87 12 

37.88 

86.95 

38.26 

95 

96 

88.37 

37.51 

88.20 

37.90 

88.04 

38.28 

87.87 

38.66 

96 

97 

89.29 

37.90 

89.12 

38.29 

88.95 

38.68 

88.79 

39.07 

97 

98 

90.21 

38.29 

90.04 

38.68 

89.87 

39.08 

89.70 

39.47 

98 

99 

91.13 

38.68 

90.96 

39.08 

90.79 

39.48 

90.62 

39.87 

99 

100 

92.05 

39.07 

91.88 

39.47 

91.71 

39.87 

91.53 

40.27 

100 

a! 

o 

Dep. I 

Lat. 

Dept 

Li3.t. 

Dep. 

Lat. 

Dep. 

Lat. 

• 

<y 

o 

ci 

73 

3 

Kssssz 

67 Deg. 

vhkosb! 

66f Deg: 

66 h Deg. 

66\ Deg. 

% 

ai 

+-> 

(fj 
• H 

Q 

.. ,rr 


3 r 














































































































TRAVERSE TABLE 


50 


a 

w " 

c-t- 

24 Dog. 

• 

24} Deg. 

24} Deg. 

24| Deg. 

O 

• 

tn 

r-t- 

£ 

3 

o 

<6 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

o 

(D 

1 

0.91 

0.41 : 

0.91 

0.41 

0.91 

0.41 

0.91 

0.42 

1 

2 

1.83 

0.81 

1.82 

0.82 

1.82 

0.83 

1.82 

0.84 

2 

3 

2.74 

1.22 

2.74 

1.23 

2.73 

1.24 

2.72 

1.26 

3 

4 

3.65 

1.63 

3.65 

1.64 

3.64 

1.66 

3.63 

1.67 

4 

5 

4.57 

2.03 

4.56 

2.05 

4.55 

2.07 

4.54 

2.09 

5 

6 

5.48 

2,44 

5.47 

,2.46 

5.46 

2.49 

5.45 

2.51 

6 

7 

6.39 

2.85 

6.38 

2.87 

6.37 

2.90 

6.36 

2.93 

7 

8 

7.31 

3.25 

7.29 

3.29 

7.28 

3.32 

7.27 

3.35 

8 

9 

8.22 

3.66 

8.21 

3.70 

8.19 

3.73 

8.17 

3.77 

9 

10 

9.14 

4.07 ] 

9.12 

4.11 

9.10 

4.15 

9.08 

4.19 

10 

11 

10.05 

4.47 

10.03 

4.52 

10.01 

4.56 

9.99 

4.61 

11 

12 

10.96 

4.88 

10.94 

4.93 

10.92 

4.98 

10.90 

5.02 

12 

13 

11.88 

5.29 

11.85 

5.34 

11.83 

5.39 

11.81 

5.44 

13 

14 

12.79 

5.69 

12.76 

5.75 

12.74 

5.81 

12.71 

5.86 

14 

15 

13.70 

6.10 

13.68 

6.16 

13.65 

6.22 

13.62 

6.28 

15 

16 

14.62 

6.51 

14.59 

6.57 

14.56 

6.64 

14.53 

6.70 

16 

17 

15.53 

6.92 

15.50 

6.98 

15.47 

7.05 

15.44 

7.12 

17 

18 

16.44 

7.32 

16.41 

7.39 

16.38 

7.46 

16.35 

7.54 

18 

19 

17.36 

7.73 

17.32 

7.80 

17.29 

7.88 

17.25 

7.95 

19 

20 

18.27 

8.13 j 

18.24 

8.21 

18.20 

8.29 

18.16 

8.37 

20 j 

21 

19.18 

8.54 j 

19.15 

8.63 

19.11 

8.71 

19.07 

8.79 

21 

22 

20.10 

8.95 

20.06 

9.04 

20.02 

9.12 

19.98 

9.21 

22 1 

23 

21.01 

9.35 

20.97 

9.45 

20.93 

9.54 

20.89 

9.63 

23 

24 

21.93 

9.76 

21.88 

9.86 

21.84 

9.95 

21.80 

10.05 

24 

25 

22.84 

10.17 

22.79 

10.27 

22.75 

10.37 

22.70 

10.47 

25 

26 

23.75 

10.58 

23.71 

10.68 

23.66 

10.78 

23.61 

10.89 

26 

: 27 

24.67 

10.98 

24.62 

11.09 

24.57 

11.20 

24.52 

11.30 

27 

28 

25.58 

11.39 

25.53 

11.50 

25.48 

11.61 

25.43 

11.72 

28 

29 

26.49 

11.80 

26.44 

11.91 

26.39 

12.03 

26.34 

12.14 

29 

30 

27.41 

12.20 

27.235 

12.32 

27.30 

12.44 

27*24 

12.56 

30 

31 

28.32 

12.61 

28.26 

12.73 

28.21 

12.86 

28.15 

12.98 

31 

32 

29.23 

13.02 

29.18 

13.14 

29.12 

13.27 

29.06 

13.40 

32 

33 

30.15 

13.42 

30.09 

13.55 

30.03 

13.68 

29.97 

13.82 

33 

34 

31.06 

13.83 

31.00 

13.96 

30.94 

14.10 

30.88 

14.23 

34 

35 

31.97 

14.24 

31.91 

14.38 

31.85 

14.51 

31.78 

14.65 

35 j 

36 

32.89 

14.64 

32.82 

14.79 

32.76 

14.93 

32.69 

15.07 

36 i 

37 

33.80 

15.05 

33.74 

15.20 

33.67 

15.34 

33.60 

15.49 

37 

38 

34.71 

15.46 

34.65 

15.61 

34.58 

15.76 

34.51 

15.91 

38 

39 

35.63 

15.86 

35.5 6 

16.02 

35.49 

16.17 

35.42 

16.33 

39 

40 

36.54 

16.27 

36.47 

16.43 

36.40 

16.59 

36.33 

16.75 

40 

41 

37.46 

16.68 

37.38 

16.84 

37.31 

17.00 

37.23 

17.16 

41 

42 

38.37 

17.08 

38*29 

17.25 

38.22 

17.42 

38.14 

17.58 

42 

43 

39.28 

17.49 

39.21 

17.66 

39.13 

17.83 

39.05 

18.00 

43 

44 

40.20 

17.90 

40.12 

18.07 

40.04 

18.25 

39.96 

18.42 

44 

45 

41.lt 

18.30 

41.03 

18.48 

40.95 

18.66 

40.87 

18.84 

45 

46 

42.02 

18.71 

41.94 

18.89 

41.86 

19.08 

41. n 

19.26 

46 

47 

42.94 

19.12 

42.85 

19.30 

42.77 

19.49 

42.68 

19.68 

47 

i 48 

43.85 

19.52 

43.76 

19.71 

43.68 

19.91 

43.59 

20.10 

48 

49 

44.76 

19.93 

44.68 

20.13 

44.59 

20.32 

44*50 

20.51 

49 

50 

45.68 

20.34 

45.59 

20.54 

45.50 

20.73 

45.41 

20.93 

50 1 

i 

6 

o 

a 

Dep. 

Lat. 

Dep* 

Lat. 

Dep. 

I Lat. 

Dep. 

Lat. 

<u 

o : 

a 

(Ml 

• "H 

66 Deg. 

65} Deg. 

1 

65} Deg. 

65} 

Deg. 

§ 

«+-> 

cn 

• H | 

Q I 
































































































TRAVERSE TABLE 


51 


G 

rji' 

r+ 

V 

S3 

24 Deg. 

24J Deg. 

• 

24^ Deg. 

24| Deg. 

e 
>—< . 

Ui 

r+ 

P 

o 

• 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

13 

O 

• 

51 

46.59 

20.74 

46.50 

20.95 

46.41 

21.15 

46.32 

21.35 

51 

52 

47.50 

21.15 

47.41 

21.36 

47.32 

21.56 

47.22 

21.77 

52 

53 

48.42 

21.56 

48.32 

21.77 

48.23 

21.98 

48.13 

22.19 

53 

54 

49.33 

21.96 

49.24 

22.18 

49.14 

22.39 

49.04 

22.61 

54 

55 

50.24 

22.37 

50.15 

22.59 

50.05 

22.81 

49.95 

23.03 

55 

56 

51.16 

22.78 

51.06 

23.00 

50.96 

23.22 

50.86 

23.44 

56 

57 

52.07 

23.18 

51.97 

23.41 

51.87 

23.64 

51.76 

23.86 

57 

58 

52.99 

23.59 

52.88 

23.82 

52.78 

24.05 

52.67 

24.28 

58 

59 

53.90 

24.00 

53.79 

24.23 

53.69 

24.47 

53.58 

24.70 

59 

GO 

54.81 

24.40 

54.71 

24.64 

54.60 

24.88 

54.49 

25.12 

60 

61 

55.73 

24.81 

55.62 

25.05 

55.51 

25.30 

55.40 

25.54 

61 

62 

56.64 

25.22 

56.53 

25.46 

56.42 

25.71 

56.30 

25.96 

62 

63 

57.55 

25.62 

57.44 

25.88 

57.33 

26.13 

57.21 

26.38 

63 

64 

58.47 

26.03 

58.35 

26.29 

58.24 

26.54 

58.12 

26.79 

64 

65 

59.38 

26.44 

59.26 

26.70 

59.15 

26.96 

59.03 

27.21 

65 

66 

60.29 

26.84 

60.18 

27.11 

60.06 

27.37 

59.94 

27.63 

66 

67 

61.21 

27.25 

61.09 

27.52 

60.97 

27.78 

60.85 

28.05 

67 

68 

62.12 

27.66 

62.00 

27.93 

61.88 

28.20 

61.75 

28.47 

68 

69 

63.03 

28.06 

62.91 

28.34 

62.79 

28.61 

62.66 

28.89 

69 

70 

63.95 

28.47 

63.82 

28.75 

63.70 

j 

29.03 

63.57 

... 

29.31 

70 

71 

64.86 

28.88 

64.74 

29.16 

64.61 

29.44 

64.48 

29.72 

71 

72 

65.78 

29.28 

65.65 

29.57 

65.52 

29.86 

65.39 

30.14 

72 

73 

66.69 

29.69 

66.56 

29.98 

66.43 

30.27 

66.29 

30.56 

73 

74 

67.60 

30.10 

67.47 

30.39 

67.34 

30.69 

67.20 

30.98 

74 

75 

68.52 

30.51 

68.38 

30.80 

68.25 

31.10 

68.11 

31.40 

75 

76 

69.43 

30-91 

69.29 

31.21 

69.16 

31.52 

69.02 

31.82 

76 

77 

70.34 

31.32 

70.21 

31.63 

70.07 

31.93 

69.93 

32.24 

77 

78 

71.26 

31.73 

71.12 

32.04 

70.98 

32.35 

70.84 

32.66 

78 

79 

72.17 

32.13 

72.03 

32.45 

71.89 

32.76 

71.74 

33.07 

79 

80 

73.08 

32.54 

72.94 

32.86 

72.80 

33.18 

72.65 

33.49 

80 

81 

74.00 

32.95 

1 73.85 

33.27 

73.71 

33.59 

73.56 

33.91 

81 

82 

74.91 

33.35 

74.76 

33.68 

74.62 

34.00 

74.47 

34.33 

82 

83 

75.82 

33.76 

75.68 

34.09 

75.53 

34.42 

75.38 

34.75 

83 

84 

76.74 

34.17 

76.59 

34.50 

76.44 

34.83 

76.28 

35.17 

84 

85 

77.65 

34.57 

77.50 

34.91 

77.35 

35.25 

77.19 

35.59 

85 

86 

78.56 

34.98 

78.41 

35.32 

78.26 

35.66 

78.10 

36.00 

86 

87 

79.48 

35.39 

79.32 

35.73 

79.17 

36.08 

79.01 

36.42 

87 

88 

80.39 

35.79 

80.24 

36.14 

80.08 

36.49 

79.92 

36.84 

88 

89 

81.31 

36.20 

81.15 

36.55 

80.99 

36.91 

80.82 

37.26 

89 

90 

82.22 

36.61 

82.06 

36.96 

81.90 

37.32 

81.73 

37.68 

90 

91 

83.13 

37.01 

82.97 

37.38 

82.81 

37.74 

82.64 

38.10 

91 

92 

84.05 

37.42 

83.88 

37.79 

83.72 

38.15 

83.55 

38.52 

92 

93 

84.96 

37.83 

84.79 

38.20 

84.63 

38.57 

84.46 

38.94 

93 

94 

85.87 

38.23 

85.71 

38.61 

85.54 

38.98 

85.37 

39.35 

94 

95 

86.79 

38.64 

86.62 

39.02 

86.45 

39.40 

86.27 

39.77 

95 

96 

87.70 

39.05 

87.53 

39.43 

87.36 

39.81 

87.18 

40.19 

96 

97 

88.61 

39.45 

88.44 

39.84 

88.27 

40.23 

88.09 

40.61 

97 

98 

89.53 

39.86 

89.35 

40.25 

89.18 

40.64 

89.00 

41.03 

98 

99 

90.44 

40.27 

90.26 

40.66 

90.09 

41.05 

89.91 

41.45 

99 

100 

91.35 

40.67 

91.18 

41.07 

91.00 

41.47 

90.81 

41.87 

100 

aj 

o 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

6 

o 

n 

Distar 

66 Deg. 

65| Deg. 

65£ Deg. 

65| Deg. 

d 

«*-> 

CO 
• pH 

Q 


































































































52 


TRAVERSE TABLE 


u 

DO 

ft- 

P 

25 Deg. 

* 

25$ 

Deg. 

25$ 

Deg. 

251 

Deg. 

O 

b-* • 

r/i 

c+ 

V 

0 

Ci 

a 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

a 

a> 

• 

1 

0.91 

0.42 

0.90 

0.43 

0.90 

0.43 

0.90 

0.43 

1 

2 

1.81 

0.85 

1.81 

0.85 

1.81 

0.86 

1.80 

0.87 

2 

3 

2.72 

1.27 

2.71 

1.28 

2.71 

1.29 

2.70 

1.30 

3 

4 

3.63 

1.69 

3.62 

1.71 

3.61 

1.72 

3.60 

1.74 

4 

5 

4.53 

2.11 

4.52 

2.13 

4.51 

2.15 

4.50 

2.17 

5 

6 

5.44 

2.54 

5.43 

2.56 

5.42 

2.58 

5.40 

2.61 

6 

7 

6.34 

2.96 

6.33 

2.99 

6.32 

3.01 

6.30 

3.04 

7 

8 

7.25 

3.38 

7.24 

3.41 

7.22 

3.44 

7.21 

3.48 

8 

9 

8.16 

3.80 

8.14 

3.84 

8.12 

3.87 

8.11 

3.91 

9 

10 

9.06 

4.23 

9.04 

4.27 

9.03 

4.31 

9.01 

4.34 

10 

11 

9.97 

4.65 

9.95 

4.69 

9.93 

4.74 

9.91 

4.78 

11 

12 

10.88 

5.07 

10.85 

5.12 

10.83 

5.17 

10.81 

5.21 

12 

13 

11.78 

5.49 

11.76 

5.55 

11.73 

5.60 

11.71 

5.65 

13 

14 

12.69 

5.92 

12.66 

5.97 

12.64 

6.03 

12.61 

6.08 

14 

15 

13.59 

6.34 

13.57 

6.40 

13.54 

6.46 

13.51 

6.52 

15 

16 

14.50 

6.76 

14.47 

6.83 

14.44 

6.89 

14.41 

6.95 

16 

17 

15.41 

7.18 

15.38 

7.25 

15.34 

7.32 

15.31 

7.39 

17 

18 

16.31 

7.61 

16.28 

7.68 

16.25 

7.75 

16.21 

7.82 

18 

19 

17.22 

8.03 

17.18 

8.10 

17.15 

8.18 

17.11 

8.25 

19 

20 

18.13 

8.45 

18.09 

8.53 

18.05 

8.61 

18.01 

8.69 

20 

21 

19.03 

8.87 

18.99 

8.96 

18.95 

9.04 

18.91 

9.12 

21 

22 

19.94 

9.30 

19.90 

9.38 

19.86 

9.47 

19.82 

9.56 

22 

23 

20.85 

9.72 

20.80 

9.81 

20.76 

9.90 

20.72 

9.99 

23 

24 

21.75 

10.14 

21.71 

10.24 

21.66 

10.33 

21.62 

10.43 

24 

25 

22.66 

10.57 

22.61 

10.66 

22.56 

10.76 

22.52 

10.86 

25 

26 

23.56 

10.99 

23.52 

11.09 

23.47 

11.19 

23.42 

11.30 

26 

27 

24.47 

11.41 

24.42 

11.52 

24.37 

11.62 

24.32 

11.73 

27 

28 

25.38 

11.83 

25.32 

11.94 

25.27 

12.05 

25.22 

12.16 

28 

29 

26.28 

12.26 

26.23 

12.37 

26.17 

12.48 

26.12 

12.60 

29 

30 

27.19 

12.68 

27.13 

12'. 80 

27.08 

12.92 

27.02 

13.03 

30 

31 

28.10 

13.10 

28.04 

13.22 

27.98 

13.35 

27.92 

13.47 

31 

32 

29.00 

13.52 

28.94 

13.65 

28.88 

13.78 

28.82 

13.90 

32 

33 

29.91 

13.95 

29.85 

14.08 

29.79 

14.21 

29.72 

14.34 

33 

34 

30.81 

14.37 

30.75 

14.50 

30.69 

14.64 

30.62 

14.77 

34 

35 

31.72 

14.79 

31.66 

14.93 

31.59 

15.07 

31.52 

15.21 

35 

36 

32.63 

15.21 

32.56 

15.36 

32.49 

15.50 

32.43 

15.64 

36 

37 

33.53 

15.64 

33.46 

15.78 

33.40 

15.93 

33.33 

16.07 

37 

38 

34.44 

16.06 

34.37 

16.21 

34.30 

16.36 

34.23 

16.51 

38 

39 

35.35 

16.48 

35.27 

16.64 

35.20 

16.79 

35.13 

16.94 

39 

40 

36.25 

16.90' 

36.18 

17.06 

36.10 

17.22 

36.03 

17.38 

40 

41 

37.16 

17.33 

37.08 

17.49 

37.01 

17.65 

36.93 

17.81 

41 

42 

38.06 

17.75 

37.99 

17.92 

37.91 

18.08 

37.83 

18.25 

42 

43 

38.97 

18.17 

38.89 

18.34 

38.81 

18.51 

38.73 

18.68 

43 

44 

39.88 

18.60 

39.80 

18.77 

39.71 

18.94 

39.63 

19.12 

44 

45 

40.78 

19.02 

40.70 

19.20 

40.62 

19.37 

40.53 

19.55 

45 

46 

41.69 

19.44 

41.60 

19.62 

41.52 

19.80 

41.43 

19.98 

46 

47 

42.60 

19.86 

42.51 

20.05 

42.42 

20.23 

42.33 

20.42 

47 

48 

43.50 

20.29 

43.41 

20.48 

43.32 

20.66 

43.23 

20.85 

48 

49 

44.41 

20.71 

44.32 

20.90 

44.23 

21.10 

44.13 

21.29 

49 

50 

45.32 

21.13 

45.22 

21.33 

45.13 

21.53 

45.03 

21.72 

50 

* 

V 

o 

c 

Dep. 

Lat. 

Dep. j 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

cu 

o 

■4~> 

CO 
• H 

Q 

65 Deg. 

64f Deg. 

64i Deg. 

64i Deg. 

S3 

(Si 

• 

O 










































































TRAVERSE TABLE 


53 


u 
»—. 

w 

r~*~ 

V 

a 

o 

n 

• 

25 Deg. 

254 Deg. 

25} Deg. 

25| Deg. | 

Distance. 

Lat. 

n 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

51 

46.22 

21.55 

46.13 

21.75 

46.03 

21.96 

45.94 

22.16 

51 

52 

47.13 

21.98 

47.03 

22.18 

46.93 

22.39 

46.84 

22.59 

52 

53 

48.03 

22.40 

47.94 

22.61 

47.84 

22.82 

47.74 

23.03 

53 

54 

48.94 

22.82 

48.84 

23.03 

48.74 

23.25 

48.64 

23.46 

54 

55 

49.85 

23.24 

49.74 

23.46 

49.64 

23.68 

49.54 

23.89 

55 

56 

50.75 

23.67 

50.65 

23.89 

50.54 

24.11 

50.44 

24.33 

56 

57 

51.66 

24.09 

51.55 

24.31 

51.45 

24.54 

51.34 

24.76 

57 

58 

52.57 

24.51 

52.46 

24.74 

52.35 

24.97 

52.24 

25.20 

58 

59 

53.47 

24.93 

53.36 

25.17 

53.25 

25.40 

53.14 

25.63 

59 

60 

54.38 

25.36 

54.27 

25.59 

54.16 

25.83 

54.04 

26.07 

60 

61 

55.28 

25.78 

55.17 

26.02 

55.06 

26.26 

54.94 

26.50 

61 

62 

56.19 

26.20 

56.08 

26.45 

55.96 

26.69 

55.84 

26.94 

62 

63 

57.10 

26.62 

56.98 

26.87 

56.86 

27.12 

56.74 

27.37 

63 

64 

58.00 

27.05 

57.89 

27.30 

57.77 

27.55 

57.64 

27.80 

64 

65 

58.91 

27.47 

58.79 

27.73 

58.67 

27.98 

58.55 

28.24 

65 

66 

59.82 

27.89 

59.69 

28.15 

59.57 

28.41 

59.45 

28.67 

66 

67 

60.72 

28.32 

60.60 

28.58 

60.47 

28.84 

60.35 

29.11 

67 

68 

61.63 

28.74 

61.50 

29.01 

61.38 

29.27 

61.25 

29.54 

68 

69 

62.54 

29.16 

62.41 

29.43 

62.28 

29.71 

62.15 

29.98 

69 

70 

63.44 

29.58 

63.31 

29.86 

63.18 

30.14 

63.05 

30.41 

70 

71 

64.35 

30.01 

64.22 

30.29 

64.08 

30.57 

63.95 

30.85 

71 

72 

65.25 

30.43 

65.12 

30.71 

64.99 

31.00 

64.85 

31.28 

72 

73 

66.16 

30.85 

66.03 

31.14 

65.89 

31.43 

65.75 

31.71 

73 

74 

67.07 

31.27 

66.93 

31.57 

66.79 

31.86 

66.65 

32.15 

74 

75 

67.97 

31.70 

67.83 

31.99 

67.69 

32.29 

67.55 

32.58 

75 

76 

68.88 

32.12 

68.74 

32.42 

68.60 

32.72 

68.45 

33.02 

76 

77 

69.79 

32.54 

69.64 

32.85 

69.50 

33.15 

69.35 

33.45 

77 

78 

70.69 

32.96 

70.55 

33.27 

70.40 

33.58 

70.25 

33.89 

78 

79 

71.60 

33.39 

71.45 

33.70 

71.30 

34.01 

71.16 

34.32 

79 

80 

72.50 

33.81 

72.36 

34.13 

72.21 

34.44 

72.06 

34.76 

80 

81 

73.41 

34.23 

73.26 

34.55 

73.11 

34.87 

72.96 

35.19 

81 

82 

74.32 

34.65 

74.17 

34.98 

74.01 

35.30 

73.86 

35.62 

82 

83 

75.22 

35.08 

75.07 

35.41 

74.91 

35.73 

74.76 

36.06 

83 

84 

76.13 

35 • 50 

75.97 

35.83 

75.82 

36.16 

75.66 

36.49 

84 

85 

77.04 

35.92 

76.88 

36.26 

76.72 

36.59 

76.56 

36.93 

85 

86 

77.94 

36.35 

77.78 

36.68 

77.62 

37.02 

77.46 

37.36 

86 

87 

78.85 

36.77 

78.69 

37.11 

78.52 

37.45 

78.36 

37.80 

87 

88 

79.76 

37.19 

79.59 

37.54 

79.43 

37.88 

79.26 

38.23 

88 

89 

80.66 

37.61 

80.50 

37.96 

80.33 

38.32 

80.16 

38.67 

89 

90 

81.57 

38.04 

81.40 

38.39 

81.23 

38.75 

81.06 

39.10 

90 

91 

82.47 

38.46 

82.31 

38.82 

82.14 

39.18 

81.96 

39.53 

91 

92 

83.38 

38.88 

83.21 

39.24 

83.04 

39.61 

82.86 

39.97 

92 

93 

84.29 

39.30 

84.11 

39.67 

83.94 

40.04 

83.76 

40.40 

93 

94 

85.19 

39.73 

85.02 

40.10 

84.84 

40.47 

84.67 

40.84 

94 

95 

86.10 

40.15 

85.92 

40.52 

85.75 

40.90 

85.57 

41.27 

95 

96 

87.01 

40.57 

86.83 

40.95 

86.65 

41.33 

86.47 

41.71 

96 

97 

87.91 

40.99 

87.73 

41.38 

87.55 

41.76 

87.37 

42.14 

97 

98 

88.82 

41.42 

88.64 

41.80 

88.45 

42.19 

88.27 

42.58 

98 

99 

89.72 

41.84 

89.54 

42.23 

89.36 

42.62 

89.17 

43.01 

99 

100 

90.63 

42.26 

90.45 

42.66 

90.26 

43.05 

90.07 

43.44 

100 

• 

© 

o 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. | 

Lat. 

Dep. 

Lat. 

6 

o 

a 

c 

d 

-*-» 

tn 

• *4 

Q 

65 Deg. 

64f Deg. 

64} Deg. 

64} Deg. 

d 

m 
•» 

Q 



































































54 TRAVERSE TABLE. 


0 

r/3 ' 

r~*- 

V 

26 Deg. 

• 

26} 

Deg. 

26} 

Deg. 

26} 

Deg. 

O 

M • 

tn 

o 

ct> 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

o 

<t> 

• 

1 

0.90 

0.44 

0.90 

0.44 

0.89 

0.45 

0.89 

0.45 

1 

2 

1.80 

0.88 

1.79 

0.88 

1.79 

0.89 

1.79 

0.90 

2 

3 

2.70 

1.32 

2.69 

1.33 

2.68 

1.34 

2.68 

1.35 

3 

4 

3.60 

1.75 

3.59 

1.77 

3.58 

1.78 

3.57 

1.80 

4 

5 

4.49 

2.19 

4.48 

2.21 

4.47 

2.23 

4.46 

2.25 

5 

6 

5.39 

2.63 

5.38 

2.65 

5.37 

2.68 

5.36 

2.70 

6 

7 

6.29 

3.07 

6.28 

3.10 

6.26 

3.12 

6.25 

3.15 

7 

8 

7.19 

3.51 

7.17 

3.54 

7.16 

3.57 

7.14 

3.60 

8 

9 

8.09 

3.95 

8.07 

3.98 

8.05 

4.02 

8.04 

4.05 

9 

10 

8.99 

4.38 

8.97 

4.42 

8.95 

4.46 

8.93 

4-50 

10 

11 

9.89 

4.82 

9.87 

4.87 

9.84 

4.91 

9.82 

4.95 

11 

12 

10.79 

5.26 

10.76 

5.31 

10.74 

5.35 

10.72 

5.40 

12 

13 

11.68 

5.70 

11.66 

5.75 

11.63 

5.80 

11.61 

5.85 

13 

14 

12.58 

6.14 

12.56 

6.19 

12.53 

6.25 

12.50 

6.30 

14 

15 

13.48 

6.58 

13.45 

6.63 

13.42 

6.69 

13.39 

6.75 

15 

16 

14.38 

7.01 

14.35 

7.08 

14.32 

7.14 

14.29 

7.20 

16 

17 

15.28 

7.45 

15.25 

7.52 

15.21 

7.59 

15.18 

7.65 

17 

18 

16.18 

7.89 

16.14 

7.96 

16.11 

8.03 

16.07 

8.10 

18 

19 

17.08 

8.33 

17.04 

8.40 

17.00 

8.48 

16.97 

8.55 

19 

20 

17.98 

8.77 

17.94 

8.85 

17.90 

8.92 

17.86 

9.00 

20 

21 

18.87 

9.21 

18.83 

9.29 

18.79 

9.37 

18.75 

9.45 

21 

22 

19.77 

9.64 

19.73 

9.73 

19.69 

9.82 

19.65 

9.90 

22 

23 

20.67 

10.08 

20.63 

10.17 

20.58 

10.26 

20.54 

10.35 

23 

24 

21.57 

10.52 

21.52 

10.61 

21.48 

10.71 

21.43 

10.80 

24 

25 

22.47 

10.96 

22.42 

11.06 

22.37 

11.15 

22.32 

11.25 

25 

26 

23.37 

11.40 

23.32 

11.50 

23.27 

11.60 

23.22 

11.70 

26 

27 

24.27 

11.84 

24.22 

11.94 

24.16 

12.05 

24.11 

12.15 

27 

28 

25.17 

12.27 

25.11 

12.38 

25.06 

12.49 

25.00 

12.60 

28 

29 

26.06 

12.71 

26.01 

12.83 

25.95 

12*94 

25.90 

13.05 

29 

30 

26.96 

13.15 

26.91 

13.27 

26.85 

13.39 

26.79 

13.50 

30 

31 

27.86 

13.59 

27.80 

13.71 

27.74 

13.83 

27.68 

13.95 

31 

32 

28.76 

14.-03 

28.70 

14.15 

28.64 

14.28 

28.58 

14.40 

32 

33 

29.66 

14.47 

29.60 

14.60 

29.53 

14.72 

29.47 

14.85 

33 

34 

30.56 

14.90 

30.49 

15.04 

30.43 

15.17 

30.36 

15.30 

34 

35 

31.46 

15.34 

31.39 

15.48 

31.32 

15.62 

31.25 

15.75 

35 

36 

32.36 

15.78 

32.29 

15.92 

32.22 

16.06 

32.15 

16.20 

36 

37 

33.26 

16.22 

33.18 

16.36 

33.11 

16.51 

33.04 

16.65 

37 

38 

34.15 

16.66 

34.08 

16.81 

34.01, 

16.96 

33.93 

17.10 

38 

39 

35.05 

17.10 

34.98 

17.25 

34.90 

17.40 

34.83 

17.55 

39 

40 

35.95 

17.53 

35.87 

17.69 

35.80 

17.85 

35.72 

18.00 

40 

41 

36.85 

17.97 

36.77 

18.13 

36.69 

18.29 

36.61 

18.45 

41 

42 

37.75 

18.41 

37.67 

18.58 

37.59 

18.74 

37.51 

18.90 

42 

43 

38.65 

18.85 

38.57 

19.02 

38.48 

19.19 

38.40 

19.35 

43 

44 

39.55 

19.29 

39.46 

19.46 

39.38 

19.63 

39.29 

19.80 

44 

45 

40.45 

19.73 

40.36 

19.90 

40.27 

20.08 

40.18 

20.25 

45 

46 

41.34 

20.17 

41.26 

20.35 

41.17 

20.53 

41.08 

20.70 

46 

47 

42.24 

20.60 

42.15 

20.79 

42.06 

20.97 

41.97 

21.15 

47 

48 

43.14 

21.04 

43.05 

21.23 

42.96 

21.42 

42.86 

21.60 

48 

49 

44.04 

21.48 

43.95 

21.67 

43.85 

21.86 

43.76 

22.05 

49 

50 

44.94 

21.92 

44.84 

22.11 

44.75 

22.31 

44.65 

22.50 

50 

cj 

o 

r* 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

-5 

o 

a 

+-» 

& 

• « 

Q 

64 Deg. 

63} 

Deg. 

j 63} 

Deg. 

63} 

Deg. 

Ct 

(ft 

c 

















































































TRAVERSE TABLE 


55 


Distance. 

26 Deg. 

261 

Deg. 

26 \ Deg. 

26$ Deg. 

Distance. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

|l 51 

45.84 

22.36 

45.74 

22.56 

45.64 

22.76 

45.54 

22.96 

51 

8 52 

46.74 

22.80 

46.64 

23.00 

46.54 

23.20 

46.43 

23.41 

52 

53 

47.64 

23.23 

47.53 

23.44 

47.43 

23.65 

47.33 

23.86 

53 

54 

48.53 

23.67 

48.43 

23.88 

48.33 

24.09 

48.22 

24.31 

54 

55 

49.43 

24.11 

49.33 

24.33 

49.22 

24.54 

49.11 

24.76 

55 

56 

50.33 

24.55 

50.22 

24.77 

50.12 

24.99 

50.01 

25.21 

56 

57 

51.23 

24.99 

51.12 

25.21 

51.01 

25.43 

50.90 

25.66 

57 

58 

52.13 

25.43 

52.02 

25.65 

51.91 

25.88 

51.79 

26.11 

58 

58 

53.03 

25.86 

52.92 

26.09 

52.80 

26.33 

52.69 

26.56 

59 

60 

53.93 

26.30 

53.81 

26.54 

53.70 

26.77 

53.58 

27.01 

60 

61 

54.83 

26.74 

54.71 

26.98 

54.59 

27.22 

54.47 

27.46 

61 

62 

55.73 

27.18 

55.61 

27.42 

55.49 

27.66 

55.36 

27.91 

62 

63 

56.62 

27.62 

56.50 

27.86 

56.38 

28.11 

56.26 

28.36 

63 

64 

57.52 

28.06 

57.40 

28.31 

57.28 

28.56 

57.15 

28.81 

64 

65 

58.42 

28.49 

58.30 

28.75 

58.17 

29.00 

58.04 

29.26 

65 

66 

59.32 

28.93 

59.19 

29.19 

59.07 

29.45 

58.94 

29.71 

66 

67 

60.22 

29.37 

60.09 

29.63 

59.96 

29.90 

59.83 

30.16 

67 

68 

61.12 

29.81 

60.99 

30.08 

60.86 

30.34 

60.72 

30.61 

68 

69 

62.02 

30.25 

61.88 

30.52 

61.75 

30.79 

61.62 

31.06 

69 

70 

62.92 

30.69 

62.78 

30.96 

62.65 

L _ _ 

31.23 

62.51 

31.51 

70 

71 

63.81 

31.12 

63.68 

31.40 

63.54 

31.68 

63.40 

31.96 

71 

72 

64.71 

31.56 

64.57 

31.84 

64.44 

32.13 

64.29 

32.41 

72 

73 

65.61 

32.00 

65.47 

32.29 

65.33 

32.57 

65.19 

32.86 

73 

74 

66.51 

32.44 

66.37 

32.73 

66.23 

33.02 

66.08 

33.31 

74 

75 

67.41 

32.88 

67.27 

33.17 

67.12 

33.46 

66.97 

33.76 

75 

76 

68.31 

33.32 

68.16 

33.61 

68.01 

33.91 

67.87 

34.21 

76 

il 

69.21 

33.75 

69.06 

34.06 

68.91 

34.36 

68.76 

34.66 

77 

78 

70.11 

34.19 

69.96 

34.50 

69.80 

34.80 

69.65 

35.11 

78 

79 

71.00 

34.63 

70.85 

34.94 

70.70 

35.25 

70.55 

35.56 

79 

80 

71.90 

35.07 

71.75 

35.38 

fa 

71.59 

35.70 

71.44 

36.01 

80 

81 

72.80 

35.51 

72.65 

35.83 

72.49 

36.14 

72.33 

36.46 

81 

82 

73.70 

35.95 

73.54 

36.27 

73.38 

36.59 

73.22 

36.91 

82 

83 

74.60 

36.38 

74.44 

36.71 

74.28 

37.03 

74.12 

37.36 

83 

84 

75.50 

36.82 

75.34 

37.15 

75.17 

37.48 

75.01 

37.81 

.84 

85 

76.40 

37.26 

76.23 

37.59 

76.07 

37.93 

75.90 

38.26 

85 

86 

77.30 

37.70 

77.13 

38.04 

76.96 

38.37 

76.80 

38.71 

86 

87 

78.20 

38.14 

78.03 

38.48 

77.86 

38.82 

77.69 

39.16 

87 

88 

79.09 

38.58 

78.92 

38.92 

78.75 

39.27 

78.58 

39.61 

88 

89 

79.99 

39.01 

79.82 

39.36 

79.65 

39.71 

79.48 

40.06 

89 

90 

80.89 

39.45 

80.72 

39.81 

80.54 

40.16 

. . i 

80.37 

40.51 

90 

91 

81.79 

39.89 | 

81.62 

40.25 

81.44 

40.60 

81.26 

40.96 

91 

92 

82.69 

40.33 

82.51 

40.69 

82.33 

41.05 

82.15 

41.41 

92 

93 

83.59 

40.77 

83.41 

41.13 

83.23 

41.50 

83.05 

41.86 

93 

94 

84.49 

41.21 

84.31 

41.58 

84.12 

41.94 

83.94 

42.31 

94 

95 

85.39 

41.65 

85.20 

42.02 

85.02 

42.39 

84.83 

42.76 

95 

96 

86.28 

42.08 

86.10 

42.46 

85.91 

42.83 

85.73 

43.21 

96 

97 

87.18 

42.52 

87.00 

42.90 

86.81 

43.28 

86.62 

43.66 

97 

98 

88.08 

42.96 

87.89 

43.34 

87.70 

43.73 

87.51 

44.11 

98 

99 

88.98 

43.40 

88.79 

43.79 

88.60 

44.17 

88.40 

44.56 

99 

100 

89.88 

43.84 

89.69 

44.23 

89.49 

44.62 

89.30 

45.01 

100 

q5 

o 

Dep. 

Lat. 

Dep. 1 

Lat. 

Dep. 1 

Lat. 

Dep. 

Lat. 

« 

V 

; a 

'n 

2 

64 Deg. j 

63| Deg. j 

63£ Deg. 

63^ Deg. 

Q 

































































































































TRAVERSE TABLE 


• 50 


la 

E c/3 

P 

27 Deg. 

27£ Deg. 

27 h Deg. 

271 Deg. 

G 

• 

C/3 

P 

o 
, o 

? 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

o 

(t> 

• 

1 

0.89 

0.45 

0.89 

0.46 

0.89 

0.46 

0.88 

0.47 

1 

2 

1.78 

0.91 

1.78 

0.92 

1.77 

0.92 

1.77 

0.93 

2 

3 

2.67 

1.36 

2.67 

1.37 

2.66 

1.39 

2.65 

1.40 

3 

4 

3.56 

1.82 

3.56 

1.83 

3.55 

1.85 

3.54 

1.86 

4 

5 

4.45 

2.27 

4.45 

2.29 

4.44 

2.31 

4.42 

2.33 

5 

6 

5.35 

2.72 

5.33 

2.75 

5.32 

2.77 

5.31 

2.79 

6 

7 

6.24 

3.18 

6.22 

3.21 

6.21 

3.23 

6.19 

3.26 

7 

8 

7.13 

3.63 

7.11 

3.66 

7.10 

3.69 

7.08 

3.72 

8 

9 

8.02 

4.09 

8.00 

4.12 

7.98 

4^16 

7.96 

4.19 

9 

10 

8.91 

4.54 

8.89 

4.58 

8.87 

4.^2 

8.85 

4.66 

10 

11 

9.80 

4.99 

9.78 

5.04 

9.76 

5.08 

9.73 

5.12 

11 

12 

10.69 

5.45 

10.67 

5.49 

10.64 

5.54 

10.62 

5.59 

12 

13 

11.58 

5.90 

11.56 

5.95 

11.53 

6.00 

11.50 

6.05 

13 

14 

12.47 

6.36 

12.45 

6.41 

12.42 

6.46 

12.39 

6.52 

14 

15 

13.37 

6.81 

13.34 

6.87 

13.31 

6.93 

13.27 

6.98 

15 

16 

14.26 

7.26 

14.22 

7.33 

14.19 

7.39 

14.16 

7.45 

16 

17 

15.15 

7.72 

15.11 

7.78 

15.08 

7.85 

15.04 

7.92 

17 

18 

16.04 

8.17 

16.00 

8.24 

15.97 

8.31 

15.93 

8.38 

18 

19 

16.93 

8.63 

16.89 

8.70 

16.85 

8.77 

16.81 

8.85 

19 | 

20 

17.82 

9.08 

17.78 

9.16 

17.74 

9.23 

17.70 

9.31 

20 

21 

18.71 

9.53 

18.67 

9.62 

18.63 

9.70 

18.58 

9.78 

21 

22 

19.60 

9.99 

19.56 

10.07 

19.51 

10.16 

19.47 

10.24 

22 

23 

20.49 

10.44 

20.45 

10.53 

20.40 

10.62 

20.35 

10.71 

23 

24 

21.38 

10.90 

21.34 

10.99 

21.29 

11.08 

21.24 

11.17 

24 

25 

22.28 

11.35 

22.23 

11.45 

22.18 

11.54 

22.12 

11.64 

25 

26 

23.17 

11.80 

23.11 

11.90 

23.06 

12.01 

23.01 

12.11 

26 

27 

24.06 

12.26 

24.00 

12.36 

23.95 

12.47 

23.89 

12.57 

27 

28 

24.95 

12.71 

24.89 

12.82 

24.84 

12.93 

24.78 

13.04 

28 

29 

25.84 

13.17 

25.78 

13.28 

25.72 

13.39 

25.66 

13.50 

29 

30 

26.73 

13.62 

26.67 

13.74 

26.61 

13.85 

26.55 

13.97 

30 

31 

27.62 

14.07 : 

27.56 

14.19 

27.50 

14.31 

27.43 

14.43 

31 

32 

28.51 

14.53 

28.45 

14.65 

28.38 

14.78 

28.32 

14.90 

32 

33 

29.40 

14.98 

29.34 

15.11 

29.27 

15.24 

29.20 

15.37 

33 

34 

30.29 

15.44 

30.23 

15.57 

30.16 

15.70 

30.09 

15.83 

34 

35 

31.19 

15.89 

31.12 

16.03 

31.05 

16.16 

30.97 

16.30 

35 

36 

32.08 

16.34 

32.00 

16.48 

31.93 

16.62 

31.86 

16.76 

36 

37 

32.97 

16.80 

32.89 

16.94 

32.82 

17.03 

32.74 

17.23 

37 

38 

33.86 

17.25 

33.78 

17.40 

33.71 

17.55 

33.63 

17.69 

38 

39 

34.75 

17.71 

34.67 

17.86 

34.59 

18.01 

34.51 

18.16 

39 

40 

35.64 

18.16 

35.56 

18.31 

35.48 

18.47 

35.40 

18.62 

40 

41 

36.53 

18.61 

36.45 

18.77 

36.37 

18.93 

36.28 

19.09 

41 

42 

37.42 

19.07 

37.34 

19.23 

37.25 

19.39 

37.17 

19.56 

42 

43 

38.31 

19.52 

38.23 

19.69 

38.14 

19.86 

38.05 

20.02 

43 

44 

39.20 

19.98 

39.12 

20.15 

39.03 

20.32 

38.94 

20.49 

44 

45 

40.10 

20.43 

40.01 

20.60 

39.92 

20.78 

39.82 

20.95 

45 

46 

40.99 

20.88 

40i89 

21.06 

40.80 

21.24 

40.71 

21.42 

46 

47 

41.88 

21.34 

41.78 

21.52 

41.69 

21.70 

41.59 

21.88 

47 

48 

42.77 

21.79 

42.67 

21.98 

42.58 

22.16 

42.48 

22.35 

48 

49 

43.66 

22.25 

43.56 

22.44 

43.46 

22.63 

43.36 

22.82 

49 

50 

44.55 

22.70 

44.45 

22.89 

44.35 

23.09 

44.25 

23.28 

50 

• 

a) 

o 

£3 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

• 

V 

o 

d 

cn 

• *—< 

Q 

63 Deg. 

— ■ ■ ■ '■ i 

62f Deg. 

62£ Deg. 

62£ Deg. 

P 

d 

CO 

G 


















































































TRAVERSE TABLE. 



O 

to * 

t-+- 

p 

1 27 Deg. 

27$ Deg. 

i 

27 h Deg. 

27| Deg. 

O 
>—. 
to 

r* 

P 


o 

CD 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

- E3 

O 

CD 

• 


51 

45.44 

23.15 

45.34 

23.35 

1 45.24 

23.55 

45.13 

23.75 

51 


52 

46.33 

23.61 

46.23 

23.81 

1 46.12 

24.01 

46.02 

24.21 

52 


53 

47.22 

24.06 

47.12 

24.27 

47.01 

24.47 

46.90 

24.68 

53 


54 

48.11 

24.52 

48.01 

24.73 

47.90 

24.93 

47.79 

25.14 

54 


55 

49.01 

24.97 

48.90 

25.18 

48.79 

25.40 

48.67 

25.61 

55 


56 

49.90 

25.42 

49.78 

25.64 

49.67 

25.86 

49.56 

26.07 

56 


57 

50.79 

25.88 

50.67 

26.10 

50.56 

26.32 

50.44 

26.54 

57 


58 

51.68 

26.33 

51.56 

26.56 

51.45 

26.78 

51.33 

27.01 

58 


59 

52.57 

26.79 

52.45 

27.01 

52.33 

27.24 

52.21 

27.47 

59 


60 

53.46 

27.24 

53.34 

27.47 

53.22 

27.70 

53.10 

27.94 

60 


61 

54.35 

27.69 

54.23 

27.93 

54.11 

| 23.17 

53.98 

28.40 

61 


62 

55.24 

28.15 

55.12 

28.39 

54.99 

28.63 

54.87 

28.87 

62 


63 

56.13 

28.60 

56.01 

28.85 

55.88 

29.09 

55.75 

29.33 

63 


64 

57.02 

29.06 

56.90 

29.30 

56.77 

29.55 

56.64 

29.80 

64 


65 

57.92 

29.51 

57.79 

29.76 

57.66 

30.01 

57.52 

30.26 

65 


66 

58.81 

29.96 

58.68 

30.22 

58.54 

30.48 

58.41 

30.73 

66 


67 

59.70 

30.42 

59.56 

30.68 

59.43 

30.94 

59.29 

31.20 

67 


68 

60.59 

30.87 

60.45 

31.14 

60.32 

31.40 

60.18 

31.66 

68 


69 

61.48 

31.33 

61.34 

31.59 

I 61.20 

31.86 

61.06 

32.13 

69 


70 

62.37 

31.78 

62.23 

32.05 

62.09 

32.32 

61.95 

32.59 

70 


71 

63.26 

32.23 

63.12 

32.51 

62.98 

| 32.78 

62.83 

33.06 

71 


72 

64.15 

32.69 

64.01 

32.97 

63.86 

33.25 

63.72 

33.52 

72 


73 

65.04 

33.14 

64.90 

33.42 

64.75 

33.71 

64.60 

33.99 

73 


74 

65.93 

33.60 

65.79 

33.88 

65.64 

34.17 

65.49 

34.46 

74 


75 

66 83 

34.05 

66.68 

34.34 

66.53 

34.63 

66.37 

34.92 

75 


76 

67.72 

34.50 

67.57 

34.80 

67.41 

1 35.09 

67.26 

35.39 

76 


77 

68.61 

34.96 

68.45 

35.26 

68.30 

1 35.55 

68.14 

35.85 

77 


78 

69.50 

35.41 

69.34 

35.71 

69.19 

36.02 

69-03 

36.32 

78 


79 

70.39 

35.87 

70.23 

36.17 j 

70.07 

36.48 

69.91 

36.78 

79 


80 

71.28 

36.32 

71.12 

36.63 

70.96 

36.94 

70.80 

37.25 

80 


81 

72.17 

36.77 

72.01 

37.09 | 

1 71.85 1 

37.40 

71.68 

37.71 

81 


82 

73.06 

37.23 

72.90 

37.55 

72.73 

37.86 

72.57 

38.18 

82 


83 

73.95 

37.68 

73.79 

38.00 

73.62 

38.33 

73.45 

38.65 

83 


84 

74.84 

38.14 

74.68 

38.46 

74.51 

38.79 

74.34 

39.11 

84 


85 

75.74 

38.59 

75.57 

38.92 1 

75.40 

39.25 

75.22 

39.58 

85 


86 

76.63 

39.04 

76.46 

39.38 

76.28 

39.71 

76.11 

40.04 

86 


87 

77.52 

39.50 

77.34 

39.83 

77.17 

40.17 

76.99 

40.51 

87 


88 

78.41 

39.95 

78.23 

40.29 

78.06 

40.63 

77.88 

40.97 

88 


89 

79.30 

40.41 

79.12 

40.75 

78.94 

41.10 

78.76 

41.44 

89 


90 

80.19 

40.86 

80.01 

41.21 

79.83 

41.56 

79.65 

41.91 

90 


91 

81.08 

41.31 

80.90 

41.67 

80.72 | 

42.02 

80.53 

42.37 

91 

92 

81.97 

41.77 

81.79 

42.12 

81.60 

42.48 

81.42 

42.84 

92 

93 

82.86 

42.22 

82.68 

42.58 

82.49 

42.94 

82.30 

43.30 

93 

1 94 

83.75 

42.68 

83.57 

43.04 

83.38 

43.40 

83.19 

43.77 

94 

95 

84.65 

43.13 

84.46 

43.50 

84.27 

43.87 

84.07 

44.23 

95 

I 96 

85.54 

43.58 

85.35 

43.96 

85.15 

44.33 

84.96 

44.70 

96 

97 

86.43 

44.04 

86.23 

44.41 

86.04 

44.79 

85.84 

45.16 

97 

I 98 

87.32 

44.49 

87.12 

44.87 

86.93 

45.25 

86.73 

45.63 

98 

I 99 

88.21 

44.95 

88.01 

45.33 

87.81 

45.71 

87.61 

46.10 

99 

110° 

89.10 

45.40 

88.90 

45.79 

88.70 

46.17 

J 

88.50 

46.56 1 

00 

II ® 

II P 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 1 

Lat. 

Dep. 

Lat. 

6 

o 

rj 

I ct5 

II on 

II *h 

II Q 

63 Deg. 

62f Deg. 

62$ Deg. 

62$ Deg. 

«S 

■4~* 

an 

5 

1 hH 

■ 


i 


I 







H 




































































































































58 


TRAVERSE TABLE. 


Distance. 

28 Deg. 

i 

284 Deg. 

I 

28£ Deg. 

1 

28£ Deg. 1 

Distance. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

1 

0.88 

0.47 

0.88 

0.47 

0.88 

0.48 

0.88 

0.48 

1 

2 

1.77 

0.94 

1.76 

0.95 

1.76 

0.95 

1.75 

0.96 

2 

3 

2.65 

1.41 

2.64 

1.42 

2.64 

1.43 

2.63 

1.44 

3 

4 

3.53 

1.88 

3.52 

1.89 

3.52 

1.91 

3.51 

1.92 

4 

5 

4.41 

2.35 

4.40 

2.37 

4.39 

2.39 

4.38 

2.40 

5 

6 

5.30 

2.82 

5.29 

2.84 

5.27 

2.86 

5.26 

2.89 

6 

7 

6.18 

3.29 

6.17 

3.31 

6.15 

3.34 

6.14 

3.37 

7 

8 

7.06 

3.76 

7.05 

3.79 

7.03 

3.82 

7.01 

3.85 

8 

9 

7.95 

4.23 

7.93 

4.26 

7.91 

4.29 

7.89 

4.33 

9 

10 

8.83 

4.69 

8.81 

4.73 

8.79 

4.77 

8.77 

4.81 

10 

11 

9.71 

5.16 

9.69 

5.21 1 

9.67 

5.25 

9.64 

5.29 

11 

12 

10.60 

5.63 

10.57 

5.68 

10.55 

5.73 

10.52 

5.77 

12 

13 

11.48 

6.10 

11.45 

6.15 I 

11.42 

6.20 

11.40 

6.25 

13 

14 

12.36 

6.57 

12.33 

6.63 j 

12.30 

6.68 

12.27 

6.73 

14 

15 

13.24 

7.04 

13.21 

7.10 1 

13.18 

7.16 

13.15 

7.21 

15 

16 

14.13 

7.51 

14.09 

7.57 

14.06 

7.63 

14.03 

7.70 

16 

17 

15.01 

7.98 

14.98 

8.05 

14.94 

8.11 

14.90 

8.18 

17 

18 

15.89 

8.45 

15.86 

8.52 

15-82 

8.59 

15.78 

8.66 

18 

19 

16.78 

8.92 

16.74 

8.99 

16.70 

9.07 

16.66 

9.14 

19 

20 

17.66 

9.39 | 

17.62 

9.47 

17.58 

9.54 

17.53 

9.62 

£0 

21 

18.54 

9.86 

18.50 

9.94 

18.46 

10.02 

18.41 

10.10 

21 

22 

19.42 

10.33 

19.38 

10.41 

19.33 

10.50 

19.29 

10.58 

22 

23 

20.31 

10.80 

20.26 

10.89 

20.21 

10.97 

20.16 

11.06 

23 

24 

21.19 

11.27 

21.14 

11.36 

21.09 

11.45 

21.04 

11.54 

24 

25 

22.07 

11.74 

22.02 

11.83 

21.97 

11.93 

21.92 

12.02 

25 

26 

22.96 

12.21 

22.90 

12.31 

22.85 

12.41 

22.79 

12.51 

26 

27 

23.84 

12.68 

23.78 

12.78 

23.73 

12.88 

23.67 

12.99 

27 

28 

24.72 

13.15 

24.66 

13.25 

24.61 

13.36 

24.55 

13.47 

28 

29 

25.61 

13.61 

25.55 

13.73 

25.49 

13.84 

25.43 

13.95 

29 

30 

26.49 

14.08 

26.43 

14.20 

26.36 

14.31 

26.30 

14.43 

30 

31 

27.37 

14.55 

27.31 

14.67 

27.24 

14.79 

27.18 

14.91 

31 

32 

28.25 

15.02 

28.19 

15.15 

28.12 

15.27 

28.06 

15.39 

32 

33 

29.14 

15.49 

29.07 

15.62 

29.00 

15.75 

28.93 

15.87 

33 

34 

30.02 

15.96 

29.95 

16.09 

29.88 

16.22 

29.81 

16.35 

34 

35 

30.90 

16.43 

30.83 

16.57 

30.76 

16.70 

30.69 

16.83 

35 

36 

31.79 

16.90 

31.71 

17.04 

31.64 

17.18 

31.56 

17.32 

36 

37 

32.67 

17.37 

32.59 

17.51 

32.52 

17.65 

32.44 

17.80 

37 

38 

33.55 

17.84 

33.47 

17.99 

33.39 

18.13 

33.32 

18.28 

38 

39 

34.43 

18.31 

34.35 

18.46 

34.27 

18.61 

34.19 

18.76 

39 

40 

35.32 

18.78 

35.24 

18.93 

35.15 

19.09 

35.07 

19.24 

40 

41 

36.20 

19.25 

36.12 

19.41 

36.03 

19.56 

35.95 

19.72 

41 

42 

37.08 

19.72 

37.00 

19.88 

36.91 

20.04 

36.82 

20.20 

42 

43 

37.97 

20.19 

37.88 

20.35 

37.79 

20.52 

37.70 

20.68 

43 

44 

38.85“ 

20.66 

38.76 

20.83 

38.67 

20.99 

38.58 

21.16 

44 

45 

39.73 

21.13 

39.64 

21.30 

39.55 

21.47 

39.45 

21.64 

45 

46 

40.62 

21.60 

40.52 

21.77 

40.43 

21.95 

40.33 

22.13 

46 

47 

41.50 

22.07 

41.40 

22.25 

41.30 

22.43 

41.21 

22.61 

47 

48 

42.38 

22.53 

42.28 

22.72 

42.18 

22.90 

42.08 

23.09 

48 

49 

43.26 

23.00 

43.16 

23.19 

43.06 

23.38 

42.96 

23.57 

49 

50 

44.15 

23.47 

44.04 

23.67 

43.94 

23.86 

43.84 

24.05 

50 

o 

o 

S3 

Dep. 

Lat. 

Dep. 

LaL 

Dep. 

Lat. 

Dep. 

Lat. 

• 

03 

O 

03 

■w 

Vi 

Q 

62 Deg. 

61J Deg. 

61^ Deg. 

6U Deg. 

V) 

• 

Q 





























































































































TRAVERSE TABLE 


59 


Distance. 

28 Deg. 

28^ Deg. 

28| Deg. 

28f Deg. 

1 Distance. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

51 

45.03 

23.94 

44.93 

24.14 

44.82 

24.34 

44.71 

24.53 

51 

52 

45,91 

24.41 

45.81 

24.61 

45.70 

24.81 

45.59 

25.01 

52 

53 

46.80 

24.88 

46.69 

25.09 

46.58 

25.29 

46.47 

25.49 

53 

54 

47.68 

25.35 

47.57 

25.56 

47.46 

25.77 

47.34 

25.97 

54 

55 

48.56 

25.82 

48.45 

26.03 

48.33 

26.24 

48.22 

26.45 

55 

56 

49.45 

26.29 

49.33 

26.51 

49.21 

26.72 

49.10 

26.94 

56 

57 

50.33 

26.76 

50.21 

26.98 

50.09 

27.20 

49.97 

27.42 

57 

58 

51.21 

27.23 

51.09 

27.45 

50.97 

27.68 

50.85 

27.90 

58 

59 

52.09 

27.70 

51.97 

27.93 

51.85 

28.15 

51.73 

28.38 

59 

60 

52.98 

28.17 

52.85 

28.40 

52.73 

28.63 

52.60 

28.86 

60 

61 

53.86 

28.64 

53.73 

28.87 

53.61 

29.11 

53.48 

29.34 

61 

62 

54.74 

29.11 

54.62 

29.35 

54.49 

29.58 

54.36 

29.82 

62 

63 

55.63 

29.58 

55.50 

29.82 

55.37 

30.06 

55.23 

30.30 

63 

64 

56.51 

30.05 

56.38 

30.29 

56.24 

30.54 

56.11 

30.78 

64 

65 

57.39 

30.52 

57.26 

30.77 

57.12 

31.02 

56.99 

31.26 

65 

66 

58.27 

30.99 

58.14 

31.24 

58.00 

31.49 

57.86 

31.75 

66 

67 

59.16 

31.45 

59.02 

31.71 

58.88 

31.97 

58.74 

32.23 

67 

68 

60.04 

31.92 

59.90 

32.19 

59.76 

32.45 

59.62 

32.71 

68 

69 

60.92 

32.39 

60.78 

32.66 

60.64 

32.92 

60.49 

33.19 

69 

70 

61.81 

32.86 

61.66 

33.13 

61.52 

33.40 

61.37 

33.67 

70 

71 

62.69 

33.33 

62.54 

33.61 

62.40 

33.88 

62.25 

34.15 

71 

72 

63.57 

33.80 

63.42 

34.08 

63.27 

34.36 

63.12 

34.63 

72 

73 

64.46 

34.27 

64.30 

34.55 

64.15 

34.83 

64.00 

35.11 

73 

74 

65.34 

34.74 

65.19 

35.03 

65.03 

35.31 

64.88 

35.59 

74 

75 

66.22 

35.21 

66.07 

35.50 

65.91 

35.79 

65.75 

36.07 

75 

76 

67.10 

35.68 

66.95 

35.97 

66.79 

36.26 

66.63 

36.56 

76 

77 

67.99 

36.15 

67.83 

36.45 

67.67 

36.74 

67.51 

37.04 

77 

78 

68.87 

36.62 

68.71 

36.92 

68.55 

37.22 

68.38 

37.52 

78 

79 

69.75 

37.09 

69.59 

37.39 

69.43 

37.70 

69.26 

38.00 

79 

80 

70.64 

37.56 

70.47 

37.87 

70.31 

38.17 

70.14 

38.48 

80 

81 

71.52 

38.03 

71.35 

38.34 

71.18 

38.65 

71.01 

38.96 

81 

82 

72.40 

38.50 

72.23 

38.81 

72.06 

39.13 

71.89 

39.44 

82 

83 

73.28 

38.97 

73.11 

39.29 

72.94 

39.60 

72.77 

39.92 

83 

84 

74.17 

39.44 

73.99 

39.76 

73.82 

40.08 

73.64 

40.40 

84 

85 

75.05 

39.91 

74.88 

40.23 

74.70 

40.56 

74.52 

40.88 

85 

86 

75.93 

40.37 

75.76 

40.71 

75.58 

41.04 

75.40 

41.36 

86 

87 

76.82 

40.84 

76-64 

41.18 

76.46 

41.51 

76.28 

41.85 

87 i 

88 

77.70 

41.31 

77.52 

41.65 

77.34 

41.99 

77.15 

42.33 

88 

89 

78.58 

41.78 

78.40 

42.13 

78.21 

42.47 

78.03 

42.81 

89 

90 

79.47 

42.25 

79.28 

42.60 

79.09 

42.94 

78.91 

43.29 

90 

91 

80.35 

42.72 

80.16 

43.07 

79.97 

43.42 

79.78 

43.77 

91 

92 

81.23 

43.19 

81.04 

43.55 

80.85 

43.90 

80.66 

44.25 

92 

93 

82.11 

43.66 

81.92 

44.02 

81.73 

44.38 

81.54 

44.73 

93 

94 

83.00 

44.13 

82.80 

44.49 

82.61 

44.85 

82.41 

45.21 

94 

95 

83.88 

44.60 

83.68 

44.97 

83.49 

45.33 

83.29 

45.69 

95 

96 

84.76 

45.07 

84.57 

45.44 

84.37 

45.81 

84.17 

46.17 

96 

97 

85.65 

45.54 

85.45 

45.91 

85.25 

46.28 

85.04 

46.66 

97 

98 

86.53 

46.01 

86.33 

46.39 

86.12 

46.76 

85.92 

47.14 

98 

99 

87.41 

46.48 

87.21 

46.86 

87.00 

47.24 

86.80 

47.62 

99 

100 

88.29 

46.95 

88.09 

47.33 

87.88 

47.72 

■... — - ■. 

87.67 

48.10 

100 

V 

o 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

<D* 

O 

d 

§ 

+-> 

Vi 

• H 

Q 

62 Deg. 

61J Deg. 

61 i Deg. 

61i Deg. 

+-> 

CO 

» w 

Q 





































































































60 


TRAVERSE TABLE 


o 

0D 

r-f- 

p 

29 Deg. 

29* 

Deg. 

29 h 

Deg. 

29f 

Deg. 

1 C 

H • 

rr> 

V 

0 

O 

tt> 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

o 

(6 

1 

0.87 

0.48 

0.87 

0.49 

0.87 

0.49 

0.87 

0.50 

1 

2 

1.75 

0.97 

1.74 

0.98 

1.74 

0.98 

1.74 

0.99 

2 

3 

2.62 

1.45 

2.62 

1.47 

2.61 

1.48 

2.60 

1.49 

3 

4 

3.50 

1.94 

3.49 

1.95 

3.48 

1.97 

3.47 

1.98 

4 

5 

4.37 

2.42 

4.36 

2.44 

4.35 

2.46 

4.34 

2.48 

5 

6 

5.25 

2.91 

5.23 

2.93 

5.22 

2.95 

5.21 

2.98 

6 

7 

6.12 

3.39 

6.11 

3.42 

6.09 

3.45 

6.08 

3.47 

7 

8 

7.00 

3.88 

6.98 

3.91 

6.96 

3.94 

6.95 

3.97 

8 

9 

7.87 

4.36 

7.85 

4.40 

7.83 

4.43 

7.81 

4.47 

9 

10 

8.75 

4.85 

8.72 

4.89 

8.70 

4.92 

8.68 

4.96 

10 

11 

9.62 

5.33 

9.60 

5.37 

9.57 

5.42 

9.55 

5.46 

11 

12 

10.50 

5.82 

10.47 

5.86 

10.44 

5.91 

10.42 

5.95 

12 

13 

11.37 

6.30 

11.34 

6.35 

11.31 

6.40 

11.29 

6.45 

13 

14 

12.24 

6.79 

12.21 

6.84 

12.18 

6.89 

12.15 

6.95 

14 

15 

13.12 

7.27 

13.09 

7.33 

13.06 

7.39 

13.02 

7.44 

15 

16 

13.99 

7.76 

13.96 

7.82 

13.93 

7.88 

13.89 

7.94 

16 

17 

14.87 

8.24 

14.83 

8.31 

14.80 

8.37 

14.76 

8.44 

17 

18 

15.74 

8.73 

15.70 

8.80 

15.67 

8.86 

15.63 

8.93 

18 

19 

16.62 

9.21 

16.58 

9.28 

16.54 

9.36 

16.50 

9.43 

19 

20 

17.49 

9.70 

17.45 

9.77 

17.41 

9.85 

17.36 

9.92 

20 

21 

18.37 

10.18 

18.32 

10.26 

18.28 

10.34 

18.23 

10.42 

21 

22 

19.24 

10.67 

19.19 

10.75 

19.15 

10.83 

19.10 

10.92 

22 

23 

20.12 

11.15 

20.07 

11.24 

20.02 

11.33 

19.97 

11.41 

23 

24 

20.99 

11.64 

20.94 

11.73 

20.89 

11.82 

20.84 

11.91 

24 

25 

21.87 

12.12 

21.81 

12.22 

21.76 

12.31 

21.70 

12.41 

25 

26 

22.74 

12.60 

22.68 

12.70 

22.63 

12.80 

22.57 

12.90 

26 

27 

23.61 

13.09 

23.56 

13.19 

23.50 

13.30 

23.44 

13.40 

27 

28 

24.49 

13.57 

24.43 

13.68 

24.37 

13.79 

24.31 

13.89 

28 

29 

25.36 

14.06 

25.30 

14.17 

25.24 

14.28 

25.18 

14.39 

29 

30 

26.24 

14.54 

26.17 

14.66 

26.11 

14.77 

26.05 

14.89 

30 

31 

27.11 

15.03 

27.05 

15.15 

26.98 

15.27 

26.91 

15.38 

31 

32 

27.99 

15.51 

27.92 

15.64 

27.85 

15.76 

27.78 

15.88 

32 

33 

28.86 

16.00 

28.79 

16.12 

28.72 

16.25 

28.65 

16.38 

33 

34 

29.74 

16.48 

29.66 

16.61 

29.59 

16.74 

29.52 

16.87 

34 

35 

30.61 

16.97 

30.54 

17.10 

30.46 

17.23 

30.39 

17.37 

35 

36 

31.49 

17.45 

31.41 

17.59 

31.33 

17.73 

31.26 

17.86 

36 

37 

32.36 

17.94 

32.28 

18.08 

32.20 

18.22 

32.12 

18.36 

37 

38 

33.24 

18.42 

33.15 

18.57 

33.07 

18.71 

32.99 

18.86 

38 

39 

34.11 

18.91 

34.03 

19.66 

33.94 

19.20 

33.86 

19.35 

39 

40 

34.98 

19.39 

34.90 

19.54 

34.81 

19.70 

34.73 

19.85 

40 

41 

35.86 

19.88 

35.77 

20.03 

35.68 

20.19 

35.60 

20.34 

41 

42 

36.73 

20.36 

36.64 

20.52 

36.55 

20.68 

36.46 

20.84 

42 

43 

37.61 

20.85 

37.52 

21.01 

37.43 

21.17 

37.33 

21.34 

43 

44 

38.48 

21.33 

38.39 

21.50 

38.30 

21.67 

38.20 

21.83 

44 

45 

39.36 

21.82 

39.26 

21.99 

39.17 

22.16 

39.07 

22.33 

45 

46 

40.23 

22.30 

40.13 

22.48 

40.04 

22.65 

39.94 

22.83 

46 

i 47 

41.11 

22.79 

41.01 

22.97 

40.91 

23.14 

40.81 

23.32 

47 

48 

41.98 

23.27 

41.88 

23.45 

41.78 

23.63 

41.67 

23.82 

48 

49 

42.86 

23.76 

42.75 

23.94 

42.65 

24.13 

42.54 

24.31 

49 

50 

43.73 

24.24 

43.62 

24.43 

43.52 

24.62 

43.41 

24.81 

50 

o 

o 

a 

Dep. j 

Lat. 

Dep. I 

Lat. 

Dep. j 

Lat. 

Dep. 

Lat. 

«> 

o 

<J) 

• rH 

Q 

61 Deg. 

60| Deg. 

60* Deg. 

60* Deg. 

c 

a 

CO 

•-H 

Q 


















































































TRAVERSE TABLE. 

( 


1 tl 

1 •—' • 

1 

i r ” 4 ' 

1 5" 

1 3 

1 29 Deg. 

29* Deg. 

1 

29* Deg. 

29J Deg. 

0 

M. 

U) 

f-+- 

1 3 

1 ? 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

P • 

o 

a 

1 51 

1 44.61 

24.73 

44.50 

24.92 

44.39 

25.11 

44.28 

25.31 

51 

I 52 

45.48 

25.21 

45.37 

25.41 

45.26 

25.61 

45.15 

25.80 

52 

I 53 

| 46.35 

25.69 

46.24 

25.90 

46.13 

26.10 

46.01 

26.30 

53 

54 

47.23 

26.18 

47.11 

26.39 

47.00 

26.59 

46.88 

26.80 

54 

I 55 

48.10 

26.66 

47.99 

26.87 

47.87 

27.08 

47.75 

27.29 

55 

1 56 

48.98 

27.15 

48.86 

27.36 

48.74 

27.58 

48.62 

27.79 

56 

57 

49.85 

27.63 

49.73 

27.85 

49.61 

28.07 

49.49 

28.28 

57 

1 58 

50.73 

28.12 

50.60 

28.34 

50.48 

28.56 

50.36 

28.78 

58 

I 59 

51.60 

28.60 

51.48 

28.83 

51.35 

29.05 

51.22 

29.28 

59 

1 60 

52.48 

29.09 

52.35 

29.32 

52.22 

29.55 

52.09 

29.77 

60 

1 61 

53.35 

29.57 

53.22 

29.81 

53.09 

30.04 

52.96 

30.27 

61 

I 62 

54.23 

30.06 

54.09 

30.29 

53.96 

30.53 

53.83 

30.77 

62 

I 63' 

55.10 

30.54 

54.97 

30.78 

54.83 

31.02 

54.70 

31.26 

63 

64 

55.98 

31.03 

55.84 

31.27 

55.70 

31.52 

55.56 

31.76 

64 

I 65 

56.85 

31.51 

56.71 

31.76 

56.57 

32.01 

56.43 

32.25 

65 

1 66 

57.72 

32.00 

57.58 

32.25 

57.44 

32.50 

57.30 

32.75 

66 

I 67 

58.60 

32.48 

58.46 

32.74 

58.31 

32.99 

58.17 

33.25 

67 

I 68 

59.47 

32.97 

59.33 

33.23 

59.18 

33.48 

59.04 

33.74 

68 

I 69 

60.35 

33.45 

60.20 

33.71 

60.05 

33.98 

59.91 

34.24 

69 

I 70 

61.22 

33.94 

61.07 

34.20 

60.92 

34.47 

60.77 

34.74 

70 

71 

62.10 

34.42 

61.95 

34.69 

61.80 

34.96 

61.64 

35.23 

71 

I 72 

62.97 

34.91 

62.82 

35.18 

62.67 

35.45 

62.51 

35.73 

72 

73 ! 

I 73 

63.85 

35.39 

63.69 

35.67 

! 63.54 

35.95 

63.38 

36.22 

1 74 

64.72 

35.88 

64.56 

36.16 

64.41 

36.44 

64.25 

36.72 

74 

75 

65.60 

36.36 

65.44 

36.65 

65.28 

36.93 

65.11 

37.22 

75 1 

l 76 

66.47 

36.85 

66.31 

37.14 

66.15 

37.42 

65.98 

37.71 

76 I 

I 77 

67.35 

37.33 

67.18 

37.62 

67.02 

37.92 

66.85 

38.21 

77 I 

I 78 

68.22 

37.82 

68.05 

38.11 

67.89 

38.41 

67.72 

38.70 

78 i 

1 79 

69.09 

38.30 

68.93 

38.60 

68.76 

38.90 

68.59 

39.20 

79 i 

I 80 

69.97 

38.78 

69.80 

39.09 

69.63 

39.39 

69.46 

39.70 

80 

I 81 

70.84 

39.27 

70.67 

39.58 

70.50 

39.89 

70.32 

40.19 

81 

82 

71.72 

39.75 

71.54 

40.07 

71.37 

40.38 

71.19 

40.69 

82 

9 83 

72.59 

40.24 

72.42 

40.56 

72.24 

40.87 

72.06 

41.19 

83 

1 84 

73.47 

40.72 

73.29 

41.04 

73.11 

41.36 

72.93 

41.68 

84 

II 85 | 

74.34 

41.21 

74.16 

41.53 

73.98 

41.86 

73.80 

42.18 

85 

II 86 | 

75.22 

41.69 

75.03 

42.02 

74.85 

42.35 

74.67 

42.67 

86 

1 87 

76.09 

42.18 

75.91 

42.51 

75.72 

42.84 

75.53 

43.17 

87 

88 

76.97 

42.66 

76.78 

43.00 

76.59 

43.33 

76.40 

43.67 

88 

1 89 

77.84 

43.15 

77.65 

43.49 

77.46 

43.83 

77.27 

44.16 

89 

I 90 

78.72 

43.63 

78.52 

43.98 

78.33 

44.32 

78.14 

44.66 

90 

I 91 

79.59 

44.12 

79.40 

44.46 

79.20 

44.81 

79.01 

45.16 

91 

1 92 

80.46 

44.60 

80.27 

44.95 

80.07 

45.30 

79.87 

45.65 

92 

I 93 

81.34 

45.09 

81.14 

45.44 

80.94 

45.80 

80.74 

46.15 

93 

1 94 

82.21 

45.57 

82.01 

45.93 

81.81 

46.29 

81.61 

46.64 

94 

1 95 

83.09 

46.06 

82.89 

46.42 

82.68 

46.78 

82.48 

47.14 

95 

II 96 | 

83.96 

46.54 

83.76 

46.91 

83.55 

47.27 

83.35 

47.64 

96 

1 97 

84.84 

47.03 | 

84.63 

47.40 

84.42 

47.77 

84.22 

48.13 

97 

| 98 

85.71 

47.51 

85.50 

47.88 

85.29 

48.26 

85.08 

48.63 

98 

1 99 

86.59 

48.00 

86.38 

48.37 

86.17 

48.75 

85.95 

49.13 

99 

1100 

87.46 

48.48 

87.25 

48.86 

87.04 

49.24 

86.82 

49.62 

100 

1 ® 

Dep. 

Lat. 

Dep. 1 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

o 

o 

c 

I w 

1 

II OT 
ll • 

II Q 1 

61 Deg. 

60f Deg. 

60* Deg. 

60* Deg. 

CT5 i 

C/3 

• 

Q 
























































































































62 TRAVERSE TABLE. 


a 

f n * 1 

r+- 

P 

30 Deg. 

f 

30i Deg. 1 

30£ Deg. 

30| Deg. 

0 

H • 

CO 

p 

s 

o 

? 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

o 

• 

1 

0.87 

0.50 

0.86 

0.50 

0.86 

0.51 

0.86 

0.51 

1 

2 

1.73 

1.00 

1.73 

1.01 

1.72 

1.02 

1.72 

1.02 

2 

3 

2.60 

1.50 

2.59 

1.51 

2.58 

1.52 

2.58 

1.53 

3 

4 

3.46 

2.00 

3.46 

2.02 

3.45 

2.03 

3.44 

2.05 

4 

5 

4.33 

2.50 

4.32 

2.52 

4.31 

2.54 

4.30 

2.56 

5 

6 

5.20 

3.00 

5.18 

3.02 

5.17 

3.05 

5.16 

3.07 

6 

7 

6.06 

3.50 

6.05 

3.53 

6.03 

3.55 

6.02 

3.58 

7 

8 

6.93 

4.00 

6.91 

4.03 

6.89 

4.06 

6.88 

4.09 

8 

9 

7.79 

4.50 

7.77 

4.53 

7.75 

4.57 

7.73 

4.60 

9 

10 

8.66 

5.00 

8.64 

5.04 

8.62 

5.08 

8.59 

5.11 

10 

11 

9.53 

5.50 

9.50 

5.54 

9.48 

5.58 

9.45 

5.62 

11 

12 

10.39 

6.00 

10.37 

6.05 

10.34 

6.09 

10.31 

6.14 

12 

13 

11.26 

6.50 

11.23 

6.55 

11.20 

6.60 

11.17 

6.65 

13 

14 

12.12 

7.00 

12.09 

7.05 

12.06 

7.11 

12.03 

7.16 

14 

15 

12.99 

7.50 

12.96 

7.56 

12.92 

7.61 

12.89 

7.67 

15 

16 

13.86 

8.00 ! 

13.82 

8.06 

13.79 

8.12 

13.75 

8.18 

16 

17 

14.72 

8.50 

14.69 

8.56 

14.65 

8.63 

14.61 

8.69 

17 

18 

15.59 

9.00 

15.55 

9.07 

15.51 

9.14 

15.47 

9.20 

18 

19 

16.45 

9.50 

16.41 

9.57 

16.37 

9.64 

16.33 

9.71 

19 

20 

17.32 

10.00 

17.28 

10.08 

17.23 

10.15 

17.19 

10.23 

20 

21 

18.19 

10.50 

18.14 

10.58 

18.09 

10.66 

18.05 

10.74 

21 

22 

19.05 

11.00 

19.00 

11.08 

18.96 

11.17 

18.91 

11.25 

22 

23 

19.92 

11.50 

19.87 

11.59 

19.82 

11.67 

19.77 

11.76 

23 

f 24 

20.78 

12.00 | 

20.73 

12.09 

1 20.68 

12.18 

20.63 

12.27 

24 

25 

21.65 

12.50 

21.60 

12.59 i 

! 21.54 

12.69 

21.49 

12.78 

25 

26 

22.52 

13.00 

22.46 

13.10 1 

1 22.40 

13.20 

22.34 

13.29 

26 

27 

23.38 

13.50 

23.32 

13.60 I 

23.26 

13.70 

23.20 

13.80 

27 

28 

24.25 

14.00 

24.19 

14.11 

| 24.13 

14.21 

24.06 

14.32 

28 

29 

25.11 

14.50 

25.05 

14.61 

1 24.99 

14.72 

24.92 

14.83 

29 

30 

25.98 

15.00 

25.92 

15.11 

j 25.85 

15.23 

25.78 

15.34 

30 

31 

26.85 

15.50 j 

26.78 

15.62 

26.71 

15.73 

26.64 

15.85 

31 

32 

27.71 

16.00 

27.64 

16.12 

27.57 

16.24 

27.50 

16.36 

32 

33 

28.58 

16.50 1 

28.51 

16.62 

28.43 

16.75 

28.36 

16.87 

33 

i 34 

29.44 

17.00 

29.37 

17.13 

29.30 

17.26 

29.22 

17.38 

34 

J 35 

30.31 

17.50 j 

30.23 

17.63 

30.16 

17.76 

30.08 

17.90 

35 

i 36 

31.18 

18.00 

31.10 

18.14 

31.02 

18.27 

30.94 

18.41 

36 

* 37 

32.04 

18.50 

31.96 

18.64 

31.88 

18.78 

31.80 

18.92 

37 

* 38 

32.91 

19.00 

32.83 

19.14 

32.74 

19.29 

32.66 

19.43 

38 

39 

33.77 

19.50 

33.69 

19.65 

33.60 

19.79 

33.52 

19.94 

39 

40 

34.64 

20.00 

34.55 

20.15 

34.47 

20.30 

34.38 

20.45 

40 

41 

35.51 

20.50 

35.42 

20.65 

35.33 

20.81 

35.24 

20.96 

41 

42 

36.37 

21.00 

36.28 

21.16 

36.19 

21.32 

36.10 

21.47 

42 

43 

37.24 

21.50 

37.14 

21.66 

37.05 

21.82 

36.95 

21.99 

43 

44 

38.11 

22.00 

38.01 

22.17 

37.91 

22.33 

37.81 

22.50 

44 

45 

38.97 

22.50 

38.87 

22.67 

38.77 

22.84 

33.67 

23.01 

45 

46 

39.84 

23.00 

39.74 

23.17 

39.63 

23.35 

39.53 

23.52 

46 

47 

40.70 

23.50 

40.60 

23.68 

40.50 

23.85 

40.39 

24.03 

47 

48 

41.57 

24.00 

41.46 

24.18 

41.36 

24.36 

41.25 

24.54 

48 

i 49 

42.44 

24.50 

42.33 

24.68 

42.22 

24.87 

42.11 

25.05 

49 

50 

43.30 

25.00 

43.19 

25.19 

43.08 

25.38 

42.97 

25.56 

50! 

o 

c 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat! 

Dep. 

Lat. 

V 

v j 

' cc 

CO 

3 

60 Deg. 

59f Deg. 

59^ Deg. 

59i Deg. 

23 

CO 1 

U) 

5 1 

t 







































































































TRAVERSE TABLE. 63 


d 

c/>* 

r+ 

P 

30 Deg. 

301 Deg. 

. 

30^ Deg. 

30J Deg. 

c 

. 

(A 

r+- 

v 

O 

<T> 

• 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

£ 

ft 

ft 

« 

51 

44.17 

25.50 

44.06 

25.69 

43.94 

25.88 

43.83 

26.08 

51 

52 

45.03 

2B.00 

44.92 

26.20 

44.80 

26.39 

44.69 

26.59 

52 

53 

45.90 

26.50 

45.78 

26.70 

45.67 

26.90 

45.55 

27.10 

53 

54 

46.77 

27.00 

46.65 

27.20 

46.53 

27.41 

46.41 

27.61 

54 

55 

47.63 

27.50 

47.51 

27.71 

47.39 

27.91 

47.27 

28.12 

55 

56 

48.50 

28.00 

48.37 

28.21 

48.25 

28.42 

48.13 

28.63 

56 

57 

49.36 

28.50 

49.24 

28.72 

49.11 

28.93 

48.99 

29.14 

57 

53 

50.23 

29.00 

.50.10 

29.22 

49.97 

29.44 

49.85 

29.65 

58 

59 

51.10 

29.50 

50.97 

29.72 

50.84 

29.94 

50.70 

30.17 

59 

60 

51.96 

30.00 

51.83 

30.23 

51.70 

30.45 

51.56 

30.68 

60 

61 

52.83 

30.50 

52.69 

30.73 

I 52.56 

30.96 

52.42 

31.19 

61 

62 

53.69 

31.00 

53.56 

31.23 

53.42 

31.47 

53.28 

31.70 

62 

63 

54.56 

31.50 

54.42 

31.74 

1 54.28 

31.97 

54.14 

32.21 

63 

64 

55.43 

32.00 

55.29 

32.24 

1 55.14 

32.48 

55.00 

32.72 

64 

65 

56.29 

32.50 

56.15 

32.75 

56.01 

32.99 

55.86 

33.23 

65 

66 

57.16 

33.00 

57.01 

33.25 

56.87 

33.50 

56.72 

33.75 

66 

67 

58.02 

33.50 

57.88 

33.75 

57.73 

34.01 

57.58 

34.26 

67 

63 

58.89 

34.00 

58.74 

34.26 

58.59 

34.51 

58.44 

34.77 

68 

69 

59.76 

34.50 

59.60 

34.76 

59.45 

35.02 

59.30 

35.28 

69 

70 

60.62 

35.00 

! 

60.47 

35.26 

60.31 

35.53 

60.16 

35.79 

70 

71 

61.49 

35.50 

61.33 

35.77 

61.18 

36.04 

61.02 

36.30 

71 

72 

62.35 

36.00 

62.20 

36.27 

62.04 

36.54 

61.88 

36.81 

72 

73 

63.22 

36.50 

63.06 

36.78 

62.90 

37.05 

62.74 

37.32 

73 

74 

64.09 

37.00 

63.92 

37.28 

63.76 

37.56 

63.60 

37.84 

74 

75 

64.95 

37.50 

64.79 

37.78 

64.62 

38.07 

64.46 

38.35 

75 

76 

65.82 

38.00 

65.65 

38.29 

65.48 

38.57 

65.31 

38.86 

76 

77 

66.68 

38.50 

h 66.52 

38.79 

66.35 

39.08 

66.17 

39.37 

77 

78 

67.55 

39.00 

67.38 

39.29 

67.21 

39.59 

67.03 

39.88 

78 

79 

68.42 

39.50 

1 68.24 

39.80 

68.07 

40.10 

67.89 

40.39 

79 

80 

69.28 

40.00 

69.11 

40.30 

68.93 

40.60 

68.75 

40.90 

80 

81 

70.15 

40.50 

69.97 

40.81 

69.79 

41.11 

69.61 

41. 

81 

82 

71.01 

41.00 

70.83 

41.31 

70.65 

41.62 

70.47 

41.93 

82 

83 

71.88 

41.50 

71.70 

41.81 

71.52 

42.13 

71.33 

42.44 

83 

84 

72.75 

42.00 

72,56 

42.32 

72.38 

42.63 

72.19 

42.95 

84 

85 

73.61 

42.50 

73.43 

42.82 

73.24 

43.14 

73.05 

43.46 

85 

86 

74.48 

43.00 

74,29 

43.32 

74.10 

43.65 

73.91 

43.97 

86 

87 

75.34 

43.50 

75.15 

43.83 

74.96 

44.16 

74.77 

44.48 

87 

88 

76.21 

44.00 

76.02 

44.33 

j 75.82 

44.66 

75.63 

44.99 

88 

89 

77.08 

44.50 

76,88 

44.84 

76.68 

45.17 

76.49 

45.51 

89 

90 

77.94 

45.00 

77.75 

45.34 

77.55 

45.68 

77.35 

46.02 

90 

91 

78.81 

45.50 

78.61 

45.84 

78.41 

46.19 

78.21 

46.53 

91 

92 

79.67 

46,00 

79.47 

46.35 

79,27 

46.69 

79.07 

47.04 

92 

93 

80.54 

46.50 

80.34 

46.85 

80.13 

47.20 

79.92 

47.55 

93 

94 

81.41 

47.00 

81.20 

47.35 

80.99 

47.71 

80.78 

48.06 

94 

95 

82.27 

47.50 

82.06 

47,86 

81.85 

48.22 

81.64 

48.57 

95 

96 

83.14 

48.00 

82.93 

48.36 

82.72 

48.72 

82.50 

49.08 

96 

97 

84.00 

48.50 

83,79 

48.87 

83.58 

49.23 

83.36 

49.60 

97 

98 

84.87 

49.00 

84.66 

49.37 

84.44 

49.74 

84.22 

50.11 

98 

99 

85.74 

49.50 

85.52 

49.87 

85.30 

50.25 

85,08 

50.62 

99 

100 

86.60 

50.00 

86.38 

50.38 

86. l£ 

50.75 

85.94 

51.13 

100 

• 

4) 

0 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lnt* 

Dep. 

Lat. 

6 

0 

c 

C 

ci 

w 

60 Deg. 

591 

Deg. 

594 Deg. 

591 Deg. 

ft 

Hi 

/■y 



V 























































































































G4 TRAVERSE TABLE. 


jj Distance. 

31 Deg. 

31$ Deg. 

31$ Deg. 

31| Deg. 

Distance. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

1 

0.86 

0.51 

0.85 

0.52 

0.85 

0.52 

0.85 

0.53 

1 

2 

1.71 

1.03 

1.71 

1.04 

1.71 

1.04 

1.70 

1.05 

2 

3 

2.57 

1.55 

2.56 

1.56 

2.56 

1.57 

2.55 

1.58 

3 

4 

3.43 

2.06 

3.42 

2.08 

3.41 

2.09 

3.40 

2.10 

4 

5 

4.29 

2.58 

4.27 

2.59 

4.26 

2.61 

4.25 

2.63 

5 

6 

5.14 

3.09 

5.13 

3.11 

5.12 

343 

5.10 

3.16 

6 

7 

6.00 

3.61 

5.98 

3.63 

5.97 

3.66 

5.95 

3.68 

7 

8 

6.86 

4.12 

6.84 

4.15 

6.82 

4.18 

6.80 

4.21 

8 

9 

7.71 

4.64 

7.69 

4.67 

7.67 

4.70 

7.65 

4.74 

9 

10 

8.57 

5.15 

8.55 

5.19 

8.53 

5.22 

8.50 

5.26 

10 

11 

9.43 

5.67 

9.40 

5.71 

9.38 

5.75 

9.35 

5.79 

11 

12 

10.29 

6.18 

10.26 

6.23 

10.23 

6.27 

10.20 

6.31 

12 

13 

11.14 

6.70 

11.11 

6.74 

11.08 

6.79 

11.05 

6.84 

13 

14 

12.00 

7.21 

11.97 

7.26 

11.94 

7.31 

11.90 

7.37 

14 

15 

12.86 

7.73 

12.82 

7.78 

12.79 

7.84 

12.76 

7.89 

15 

16 

13.71 

8.24 

13.68 

8.30 

13.64 

8.36 

13.61 

8.42 

16 

17 

14.57 

8.76 

14.53 

8.82 

14.49 

8.88 

14.46 

8.95 

17 

18 

15.43 

9.27 

15.39 

9.34 

15.35 

9.40 

15.31 

9.47 

18 

19 

16.29 

9.79 

16.24 

9.86 

16.20 

9.93 

16.16 

10.00 

19 

20 

17.14 

10.30 

17.10 

10.38 

17.05 

10.45 

17.01 

10.52 

20 

21 

18.00 

10.82 

17.95 

10.89 

17.91 

10.97 

17.86 

11.05 

21 

22 

18.86 

11.33 

18.81 

11.41 

18.76 

11.49 

18.71 

11.58 

22 

23 

19.71 

11.85 

19.66 

11.93 

19.61 

12.02 

19.56 

12.10 

23 

24 

20.57 

12.36 

20.52 

12.45 

20.46 

12.54 

20.41 

12.63 

24 

25 

21.43 

12.88 

21.37 

12.97 

21.32 

13.06 

21.26 

13.16 

25 

26 

22.29 

13.39 

22.23 

13.49 

22.17 

13.58 

22.11 

13.68 

26 

27 

23.14 

13.91 

23.08 

14.01 

23.02 

14.11 

22.96 

14.21 

27 

28 

24.00 

14.42 

23.94 

14.53 

23.87 

14.63 

23.81 

14.73 

28 

29 

24.86 

14.94 

24.79 

15.04 

24.73 

15.15 

24.66 

15.26 

29 

30 

25.71 

15.45 

25.65 

15.56 

25.58 

15.67 

25.51 

15.79 

30 

31 

Jfe.57 

15.97 

26.50 

16.08 

26.43 

16.20 

26.36 

16.31 

31 

32 

27.43 

16.48 

27.36 

16.60 

27.28 

16.72 

27.21 

16.84 

32 

33 

28.29 

17.00 

28.21 

17.12 

28.14 

17.24 

28.06 

17.37 

33 

34 

29.14 

17.51 

29.07 

17.64 

28.99 

17.76 

28.91 

17.89 

34 

35 

30.00 

18.03 

29.92 

18.16 

29.84 

18.29 

29.76 

18.42 

35 

36 

30.86 

18.54 

30.78 

18.68 

30.70 

18.81 

30.61 

18.94 

36 

37 

31.72 

19.06 

31.63 

19.19 

31.55 

19.33 

31.46 

19.47 

37 

38 

32.57 

19.57 

32.49 

19.71 

32.40 

19.85 

32.31 

20.00 

38 

39 

33.43 

20.09 

33.34 

20.23 

33.25 

20.38 

33.16 

20.52 

39 

40 

34.29 

20.60 

34.20 

20.75 

34.11 

20.90 

34.01 

21.05 

40 \ 

41 

35.14 

21.12 

35.05 

21.27 

34.96 

21.42 

34.86 

21.57 

41 ? 

42 

36.00 

21.63 

35.91 

21.79 

35.81 

21.94 

35.71 

22.10 

42 

43 

36.86 

22.15 

36.76 

22.31 

36.66 

22.47 

36.57 

22.63 

43 

44 

37.72 

22.66 

37.62 

22.83 

37.52 

22.99 

37.42 

23.15 

44 

45 

38.57 

23.18 

38.47 

23.34 

38.37 

23.51 

38.27 

23.68 

45 

46 

39.43 

23.69 

39.33 

23.86 

39.22 

24.03 

39.12 

24.21 

46 I 

47 

40.29 

24.21 

40.18 

24.38 

40.07 

24.56 

39.97 

24.73 

47 

48 

41.14 

24.72 

41.04 

24.90 

40.93 

25.08 

40.82 

25.26 

48 I 

49 

42.00 

25.24 

41.89 

25.42 

41.78 

25.60 

41.67 

25.78 

49 

50 

42.86 

25.75 

42.75 

25.94 

42.63 

26.12 

42.52 

26.31 

50 j 

Distance. 

Dep. I 

Lat. 

Depi 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

6 I 

0 I 

S3 I 

a I 

-*-> 1 

to 
• ^ 

Q 

59 Deg. 

58$ Deg. 

58$ Deg. 

58$ Deg. 


/ 
























































































TRAVERSE TABLE 


65 


I u 

1 •— • 

1 W) 

« r-► 

I ^ 

31 Deg. 

- .. .. . . . 

31* Deg. 

31 i Deg. 

31| Deg. 

0 

H . 

to 

p 

o 

a 

Lat. 

Dep. 

.L lit* 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

3 

a 

n 

• 

51 

43.72 

26.27 

43.60 

26.46 

43.48 

26.65 

43.37 

26.84 

51 

52 

44.57 

26.78 

44.46 

26.98 

44.34 

27.17 

44.22 

27.36 

52 

53 

45.43 

27.30 

45.31 

27.49 

45.19 

27.69 

45.07 

27.89 

53 

54 

46.29 

27.81 

46.17 

28.01 

46.04 

28.21 

45.92 

28.42 

54 

55 

47.14 

28.33 

47.02 

28.53 

46.90 

28.74 

46.77 

28.94 

55 

56 

48.00 

28.84 

47.88 

29.05 

47.75 

29.26 

47.62 

29.47 

56 

57 

48.86 

29.36 

48.73 

29.57 

48.60 

29.78 

48.47 

29.99 

57 

58 

49.72 

29.87 

49.58 

30.09 

49.45 

30.30 

49.32 

30.52 

58 

59 

50.57 

30.39 

50.44 

30.61 

50.31 

30.83 

50.17 

31.05 

59 

60 

51.43 

30.90 

51.29 

31.13 

51.16 

31.35 

51.02 

31.57 

60 

61 

52.29 

31.42 

52.15 

31.65 

52.01 

31.87 

51.87 

32.10 

61 

62 

53.14 

31.93 

53.00 

32.16 

52.86 

32.39 

52.72 

32.63 

62 

63 

54.00 

32.45 

53.86 

32.68 

53.72 

32.92 

53.57 

33.15 

63 

64 

54.86 

32.96 

54.71 

33.20 

54.57 

33.44 

54.42 

33.68 

64 

1 65 

55.72 

33.48 

55.57 

33.72 

55.42 

33.96 

55.27 

34.20 

65 

1 66 

56.57 

33.99 

56.42 

34.24 

56.27 

34.48 

56.12 

34.73 

66 

67 

57.43 

34.51 

57.28 

34.76 

57.13 

35.01 

56.98 

35.26 

67 

68 

58.29 

35.02 

58.13 

35.28 

57.98 

35.53 

57.82 

35.78 

68 

69 

59.14 

35.54 

58.99 

35.80 

58.83 

36.05 

58.67 

36.31 

69 

70 

60.00 

36.05 

' 59.84 

36.31 

59.68 

36.57 

59.52 

36.83 

70 

71 

60.86 

36.57 

60.70 

36.83 

60.54 

37.10 

60.37 

37.36 

71 

72 

61.72 

37.08 

61.55 

37.35 

61.39 

37.62 

61.23 

37.89 

72 

73 

62.57 

37.60 

62.41 

37.87 

62.24 

38.14 

62.08 

38.41 

73 

74 

63.43 

38.11 

63.26 

38.39 

63.10 

38.66 

62.93 

38.94 

74 

75 

64.29 

38.63 

64.12 

38.91 

63.95 

39.19 

63.78 

39.47 

75 

76 

65.14 

39.14 

64.97 

39.43 

64.80 

39.71 

64.63 

39.99 

76 

77 

66.00 

39.66 

65.83 

39.95 

65.65 

40.23 

65.48 

40.52 

77 

78 

66.86 

40.17 

66.68 

40.46 

66.51 

40.75 

66.33 

41.04 

78 

79 

67.72 

40.69 

67.54 

40.98 

67.36 

41.28 

67.18 

41.57 

79 

80 

68.57 

41.20 

68.39 

41.50 

68.21 

41.80 

68.03 

42.10 

80 

81 

69.43 

41.72 

69.25 

42.02 

69.06 

42.32 

68.88 

42.62 

81 

82 

70.29 

42.23 

70.10 

42.54 

69.92 

42.84 

69.73 

43.15 

82 

83 

71.14 

42.75 

70.96 

43.06 

70.77 

43.37 

70.58 

43.68 

83 

84 

72.00 

43.26 

71.81 

43.58 

71.62 

43.89 

71.43* 

44.20 

84 

85 

72.86 

43.78 

72.67 

44.10 

72.47 

44.41 

72.28 

44.73 

85 

86 

73.72 

44.29 

73.52 

44.61 

73.33 

44.93 

73.13 

45.25 

86 

87 

74.57 

44.81 

74.38 

45.13 

74.18 

45.46 

73.98 

45.78 

87 

88 

75.43 

45.32 

75.23 

45.65 

75.03 

45.98 

74.83 

46.31 

88 

89 

76.29 

45.84 

76.09 

46.17 

75.88 

46.50 

75.68 

46.83 

89 

90 

77.15 

46.35 

76.94 

46.69 

76.74 

47.02 

76.53 

47.36 

90 

91 

78.00 

46.87 

77.80 

47.21 

77.59 

47.55 

77.38 

47.89 

91 

92 

78.86 

47.38 

78.65 

47.73 

78.44 

48.07 

78.23 

48.41 

92 

93 

79.72 

47.90 

79.51 

48.25 

79.30 

48.59 

79.08 

48.94 

93 

94 

80.57 

48.41 

80.36 

48.76 

80.15 

49.11 

79.93 

49.47 

94 

95 

81.43 

48.93 

81.22 

49.28 

81.00 

49.64 

80.78 

49.99 

95 

96 

82.29 

49.44 

82.07 

49.80 

81.85 

50.16 

81.63 

50.52 

96 

97 

83.15 

49.96 

82.93 

50.32 

82.71 

50.68 

82.48 

51.04 

97 

98 

84.00 

50.47 

83.78 

50.84 

83.56 

51.20 

83.33 

51.57 

98 

99 

84.86 

50.99 

84.64 

51.36 

84.41 

51.73 

84.18 

52.10 

99 

100 

85.72 

51.50 

85.49 

51.88 

85.26 

52.25 

85.04 

52.62 

. 

100 

6 

o 

Dep. 1 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

6 

o 

£3 

d 

on 

3 

59 Deg. 

58| Deg. 

I! 

—-— . ■ - - ... 

---, 

58* Deg. j 

58* Deg. 

d 

li 


I 




















































































































66 


TRAVERSE TABLE 


d 

H- • 

in 

& 

32 Deg. 

32i Deg. 

32i Deg. 

32| Deg. 

d 
►— • 
in 
r*- 

P 

3 

3 

o 

a 

Lat. 

Dep. 

Lat. 

- - 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

o 

n> 

1 

0.85 

0.53 

0.85 

0.53 

0.84 

0.54 

0.84 

0.54 

1 

2 

1.70 

1.06 

1.69 

1.07 

1.69 

1.07 

1.68 

1.08 

2 

3 

2.54 

1.59 

2.54 

1.60 

2.53 

1.61 

2.52 

1.62 

3 

4 

3.39 

2.12 

3.38 

2.13 

3.37 

2.15 

3.36 

2.16 

4 

5 

4.24 

2.65 

4.23 

2.67 

4.22 

2.69 

4.21 

2.70 

5 

6 

5.09 

3.18 

5.07 

3.20 

5.06 

3.22 

5.05 

3.25 

6 

7 

5.94 

3.71 

5.92 

3.74 

5.90 

3.76 

5.89 

3.79 

7 

8 

6.78 

4.24 

6.77 

4.27 

6.75 

4.30 

6.73 

4.33 

8 

' 9 

7.63 

4.77 

7.61 

4.80 

7.59 

4.84 

7.57 

4.87 

9 

10 

8.48 

5.30 

8.46 

5.34 

8.43 

5.37 

8.41 

5.41 

10 

11 

9.33 

5.83 

9.30 

5.87 

9.28 

5.91 

9.25 

5.95 

11 

12 

10.18 

6.36 

10.15 

6.40 

10.12 

6.45 

10.09 

6.49 

12 

13 

11.02 

6.89 

10.99 

6.94 

10.96 

6.98 

10.93 

7.03 

13 

14 

11.87 

7.42 

11.84 

7.47 

11.81 

7.52 

11.77 

7.57 

14 

15 

12.72 

7.95 

12.69 

8.00 

12.65 

8.06 

12.62 

8.11 

15 

16 

13.57 

8.48 

13.53 

8.54 

13.49 

8.60 

13.46 

8.66 

16 

17 

14.42 

9.01 

14.38 

9.07 

14.34 

9.13 

14.30 

9.20 

17 

18 

15; 26 

9.54 

15.22 

9.61 

15.18 

9.67 

15.14 

9.74 

18 

19 

16.11 

10.07 

16.07 

10.14 

16.02 

10.21 

15.98 

10.28 

19 

20 

16.96 

10.60 

16.91 

10.67 

16.87 

10.75 

16.82 

10.82 

20 

21 

17.81 

11.13 

17.76 

11.21 

17.71 

11.28 

17.66 

11.36 

21 

22 

18.66 

11.66 

18.61 

11.74 

18.55 

11.82 

18.50 

11.90 

22 

23 

19.51 

12.19 

19.45 

12.27 

19.40 

12.36 

19.34 

12.44 

23 

24 

20.35 

12.72 

20.30 

12.81 

20.24 

12.90 

20.18 

12.98 

24 

25 

21.20 

13.25 

21.14 

13.34 

21.08 

13.43 

21.03 

13.52 

25 

26 

22.05 

13.78 

21.99 

13.87 

21.93 

13.97 

21.87 

14.07 

26 

27 

22.90 

14.31 

22.83 

14.41 

22.77 

14.51 

22.71 

14.61 

27 

28 

23.75 

14.84 

23.68 

14.94 

23.61 

15.04 

23.55 

15.15 

28 

29 

24.59 

15.37 

24.53 

15.47 

24.46 

15.58 

24.39 

15.69 

29 

30 

25.44 

15.90 

25 ;37 

16.01 

25.30 

16.12 

25.23 

16.23 

30 

31 

26.29 

16.43 

26.22 

16.54 

26.15 

16.66 

26.07 

16.77 

31 

32 

27.14 

16.96 

27.06- 

17.08 

26.99 

17.19 

26.91 

17.31 

32 

33 

27.99 

17.49 

27.91 

17.61 

27.83 

17.73 

27.75 

17.85 

33 

34 

28.83 

18.02 

28.75 

18.14 

28.68 

18.27 

28.60 

18.39 

34 

35 

29.68 

18.55 

29.60 

18.68 

29.52 

18.81 

29.44 

18.93 

35 

36 

30.53 

19.08 

30.45 

19.21 

30.36 

19.34 

30.28 

19.48 

36 

37 

31.38 

19.61 

31.29 

19.74 

31.21 

19.88 

31.12 

20.02 

37 

38 

32.23 

20.14 

32.14 

20.28 

32.05 

20.42 

31.96 

20.56 

'38 

39 

33.07 

20.67 

32.98 

20.81 

32.89 

20.95 

32.80 

21.10 

39 

40 

33.92 

21.20 

33.83 

21.34 

33.74 

21.49 

33.64 

21.64 

40 

41 

34.77 

21.73 

34.67 

21.88 

34.58 

22.03 

34.48 

22.18 

41 

42 

35.62 

22.26 

35.52 

22.41 

35.42 

22.57 

35.32 

22.72 

42 

43 

36.47 

22.79 

36.37 

22.95 

36.27 

23.10 

36.16 

23.26 

43 

44 

37.31 

23.32 

37.21 

23.48 

37.11 

23.64 

37.01 

23.80 

44 

45 

38.16 

23.85 

38.06 

24.01 

37.95 

24.18 

37.85 

24.34 

45 

46 

39.01 

24.38 

38.90 

24.55 

38.80 

24.72 

38.69 

24.88 

46 

47 

39.86 

24.91 

39.75 

25.08 

39.64 

25.25 

39.53 

25.43 

47 

48 

40.71 

25.44 

40.59 

25.61 

40.48 

25.79 

40.37 

25.97 

48 

49 

41.55 

25.97 

41.44 

26.15 

41.33 

26.33 

41.21 

26.51 

49 

50 

42.40 

26.50 

42.29 

26.68 

42.17 

26.86 

42.05 

27.05 

50 

a; 

o 

d 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

6 

o 

a 

■4-J 

c n 

• -H 

Q 

58 Deg. 

57 J 

Deg. 

57* 

Deg. 

574 

Deg. 

s 

a 

+-> 

C/3 
• •—< 

Q 














































































TRAVERSE TABLE. 


67 


1 e 

fl «> 

1 

1 ^ 

1 m 

32 Deg. 

32i 

Deg. 

32£ Deg. 

32f Deg. 

e 

• 

CO 

W 

i o 

i ^ 

■ 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

S3 

O 

<D 

• 

|| 51 

43.25 

27.03 

43.13 

27.21 

43.01 

27.40 

42.89 

27.59 

51 

52 

44.10 

27.56 

43.98 

27.75 

43.86 

27.94 

43.73 

28.13 

52 

| 53 

44.95 

28.09 

44.82 

28.28 

44.70 

28.48 

44.58 

28.67 

53 

| 54 

45.79 

28.62 

45.67 

28.82 

45.54 

29.01 

45.42 

29.21 

54 

I 55 

46.64 

29.15 

46.51 

29.35 

46.39 

29.55 

46.26 

29.75 

55 

1 56 

47.49 

29.68 

47.36 

29.88 

47.23 

30.09 

47.10 

30.29 

56 

| 57 

48.34 

30.21 

48.21 

30.42 

48.07 

30.63 

47.94 

30.84 

57 

| 58 

49.19 

30.74 

49.05 

30.95 

48.92 

31.16 

48.78 

31.38 

58 

59 

50.03 

31.27 

49.90 

31.48 

49.76 

31.70 

49.62 

31.92 

59 

I 60 

50.88 

31.80 

50.74 

i 

32.02 

50.60 

32.24 

50.46 

32.46 

60 

1 61 

51.73 

32.33 

51.59 

32.55 

51.45 

32.78 

51.30 

33.00 

61 

L 62 

52.58 

32.85 

52.44 

33.08 

52.29 

33.31 

52.14 

33.54 

62 

I 63 

53.43 

33.38 

53.28 

33.62 

53.13 

33.85 

52.99 

34.08 

63 

| 64 

54.28 

33.91 

54.13 

34.15 

53.98 

34.39 

53.83 

34.62 

64 

| 65 

55.12 

34.44 

54.97 

34.68 

54.82 

34.92 

54.67 

35.16 

65 

;] 66 

55.97 

34.97 

55.82 

35.22 

55.66 

35.46 

55.51 

35.70 

66 

I 67 

56.82 

35.50 

56.66 

35.75 

56.51 

36.00 

56.35 

36.25 

67 

L 68 

57.67 

36.03 

57.51 

36.29 

57.35 

36.54 

57.19 

36.79 

68 

I 69 

58.52 

36.56 

58.36 

36.82 

58.19 

37.07 

58.03 

37.33 

69 

1 70 

59.36 

37.09 

59.20 

37.35 

59.04 

37.61 

58.87 

37.87 

70 

1 71 

60.21 

37.62 

60.05 

37.89 

59.88 

38.15 

59.71 

38.41 

71 

I 72 

61.06 

38.15 

60.89 

38.42 

60.72 

38.69 

60.55 

38.95 

72 

1 73 

61.91 

38.68 

61.74 

38.95 

61.57 

39.22 

61.40 

39.49 

73 

I 74 

62.76 

39.21 

62.58 

39.49 

62.41 

39.76 

62.24 

40.03 

74 

75 

63.60 

39.74 

63.43 

40.02 

63.25 

40.30 

63.08 

40.57 

75 

1 76 

64.45 

40.27 

64.28 

40.55 

64.10 

40.83 

63.92 

41.11 

76 

I 77 

65.30 

40.80 

65.12 

41.09 

64.94 

41.37 

64.76 

41.65 

77 

78 

66.15 

41.33 

65.97 

41.62 

65.78 

41.91 

65.60 

42.20 

78 

1 79 

67.00 

41.86 

66.81 

42.16 

66.63 

42.45 

66.44 

42.74 

79 

1 80 

67.84 

42.39 

67.66 

42.69 

67.47 

42.98 

67.28 

43.28 

80 

j 81 

68.69 

42.92 

68.50 

43.22 

68.31 

43.52 

68.12 

43.82 

81 

! 82 

69.54 

43.45 

69.35 

43.76 

69.16 

44.06 

68.97 

44.36 

82 

1 83 

70.39 

43.98 

70.20 

44.29 

70.00 

44.60 

69.81 

44.90 

83 

{ 84 

71.24 

44.51 

71.04 

44.82 

70.84 

45.13 

70.65 

45.44 

84 

85 

72.08 

45.04 

71.89 

45.36 

71.69 

45.67 

71.49 

45.98 

85 

86 

72.93 

45.57 

72.73 

45.89 

72.53 

46.21 

72.33 

46.52 

86 

87 

73.78 

46.10 

73.58 

46.42 

73.38 

46.75 

73.17 

47.06 

87 

f 88 

74.63 

46.63 

74.42 

46.96 

74.22 

47.28 

74.01 

47.61 

88 

89 

75.48 

47.16 

75.27 

47.49 

75.06 

47.82 

74.85 

48.15 

89 

90 

76.32 

47.69 

76.12 

48.03 

75.91 

48.36 

75.69 

48.69 

90 

91 

77.17 

48.22 

76.96 

48.56 

76.75 

48.89 

76.53 

49.23 

91 

92 

78.02 

48.75 

77.81 

49.09 

77.59 

49.43 

77.38 

49.77 

92 

93 

78.87 

49.28 

78.65 

49.63 

78.44 

49.97 

78.22 

50.31 

93 

! 94 

79.72 

49.81 

79.50 

50.16 

79.28 

50.51 

79.06 

50.85 

94 I 

95 

80.56 

50.34 

80.34 

50.69 

80.12 

51.04 

79.90 

51.39 

95 

96 

81.41 

50.87 

81.19 

51.23 

80.97 

51.58 

80.74 

51.93 

96 

97 

82.26 

51.40 

82.04 

51.76 

81.81 

52.12 

81.58 

52.47 

97 

98 

83.11 

51.93 

82.88 

52.29 

82.65 

52.66 

82.42 

53.02 

98 

99 

83.96 

52.46 

83.73 

52.83 

83.50 

53.19 

83.26 

53.56 

99 

100 

84.80 

52.99 

84.57 

53.36 

84.34 

53.73 

84.10 

54.10 

100 

<u 

o 

Dep. 1 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

« 

o 

c 

c 

C5 

Q 

58 Deg. 

57| Deg. 

57£ Deg. 

57^ Deg. 

CO 

Q 
































































































































TRAVERSE TABLE 


63 


0 

H • 

Ui 

r+- 

9> 

33 Deg. 

33$ Deg. 

33$ Deg. 

33$ Deg. 

V 

e 
»-* . 
t D 
r+ 

V 

a 

o 

<T> 

• 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

o 

tt> 

1 

0.84 

0.54 

0.84 

0.55 

0.83 

0.55 

0.83 

0.56 

1 

2 

1.68 

1.09 

1.67 

1.10 

1.67 

1.10 

1.66 

1.11 

2 

3 

2.52 

1.63 

2.51 

1.64 

2.50 

1.66 

2.49 

1.67 

3 

4 

3.35 

2.18 

3.35 

2.19 

3.34 

2.21 

3.33 

2.22 

4 

5 

4.19 

2.72 

4.18 

2.74 

4.17 

2.76 

4.16 

2.78 

5 

6 

5.03 

3.27 

5.02 

3.29 

5.00 

3.31 

4.99 

3.33 

6 j 

7 

5.87 

3.81 

5.85 

3.84 

5.84 

3.86 

5.82 

3.89 

7 ! 

8 

6.71 

4.36 

6.69 

4.39 

6.67 

4.42 

6.65 

4.44 

8 

9 

7.55 

4.90 

7.53 

4.93 

7.50 

4.97 

7.48 

5.00 

9 : 

10 

8.39 

5.45 

8.36 

5.48 

8.34 

5.52 

8.31 

5.56 

10 

11 

9.23 

5.99 

9.20 

6.03 

9.17 

6.07 

9.15 

6.11 

11 

12 

10.06 

6.54 

10.04 

6.58 

10.01 

6.62 

9.98 

6.67 

12 

13 

10-90 

7.08 

10.87 

7.13 

10.84 

7.18 

10.81 

7.22 

13 

14 

11.74 

7.62 

11.71 

7.68 

11.67 

7.73 

11.64 

7.78 

14 ; 

15 

12.58 

8.17 

12.54 

8.22 

12.51 

8.28 

12.47 

8.33 

15 

16 

13.42 

8.71 

13.38 

8.77 

13.34 

8.83 

13.30 

8.89 

16 

17 

14.26 

9.26 

14.22 

9.32 

14.18 

9.38 

14.13 

9.44 

17 

18 

15.10 

9.80 

15.05 

9.87 

15.01 

9.93 

14.97 

10.00 

18 

19 

15.93 

10.35 

15.89 

10.42 

15.84 

10.49 

15.80 

10.56 

19 

20 

16.77 

X 

10.89 

16.73 

10.97 

16.68 

11.04 

16.63 

11.11 

20 

21 

17.61 

11.44 

17.56 

11.51 

17.51 

11.59 

17.46 

11.67 

21 

22 

18.45 

11.98 

18.40 

12.06 

18.35 

12.14 

18.29 

12.22 

22 1 

23 

19.29 

12.53 

19.23 

12.61 

19.18 

12.69 

19.12 

12.78 

23 

24 

20.13 

13.07 

20.07 

13.16 

20.01 

13.25 

19.96 

13.33 

24 

25 

20.97 

13.62 

20.91 

13.71 

20.85 

13.80 

20.79 

13.89 

25 

26 

21.81 

14.16 

21.74 

14.26 

21.68 

14.35 

21.62 

14.44 

26 

27 

22.64 

14.71 

22.58 

14.80 

22.51 

14.90 

22.45 

15.00 

27 

28 

23.48 

15.25 

23.42 

15.35 

23.35 

15.45 

23.28 

15.56 

28 

29 

24.32 

15.79 

24.25 

15.90 

24.18 

16.01 

24.11 

16.11 

29 

30 

25.16 

16.34 

25.09 

16.45 

25.02 

16.56 

24.94 

16.67 

30 

31 

26.00 

16.88 

25.92 

17.00 

25.85 

17.11 

25.78 

17.22 

31 

32 

26.84 

17.43 

26.76 

17.55 

26.68 

17.66 

26.61 

17.78 

32 

33 

27.68 

17.97 

27.60 

18.09 

27.52 

18.21 

27.44 

18.33 

33 

34 

28.51 

18.52 

28.43 

18.64 

28.35 

18.77 

28.27 

18.89 

34 

35 

29.35 

19.06 

29.27 

19.19 

29.19 

19.32 

29.10 

19.44 

35 

36 

30.19 

19.61 

30.11 

19.74 

30.02 

19.87 

29.93 

20.00 

36 

37 

31.03 

20.15 

30.94 

20.29 

30.85 

20.42 

30.76 

20.56 

37 

38 

31.87 

20.70 

31.78 

20.84 

31.69 

20.97 

31.60 

21.11 

38 

39 

32.71 

21.24 

32.62 

21.38 

32.52 

21.53 

32.43 

21.67 

39 

40 

33.55 

21.79 

33.45 

21.93 

33.36 

22.08 

33.26 

22.22 

40 

41 

34.39 

22.33 

34.29 

22.48 

34.19 

22.63 

34.09 

22.78 

41 

42 

35.22 

22.87 

35.12 

23.03 

35.02 

23.18 

34.92 

23 ♦ 33 

42 

43 

36.06 

23.42 

35.96 

23.58 

35.86 

23.73 

35.75 

23.89 

43 

44 

36.90 

23.96 

36.80 

24.12 

36.69 

24.29 

36.58 

24.45 

44 

45 

37.74 

24.51 

37.63 

24.67 

37.52 

24.84 

37.42 

25.00 

45 

46 

38.58 

25.05 

38.47 

25.22 

38.36 

25.39 

38.25 

25.56 

46 

47 

39.42 

25.60 

39.31 

25.77 

39.19 

25.94 

39.08 

26.11 

47 

" 48 

40.26 

26.14 

40.14 

26.32 

40.03 

26.49 

39.91 

26.67 

48 

49 

41.09 

26.69 

40.98 

26.87 

40.86 

27.04 

40.74 

27.22 

49 

50 

41.93 

27.23 

41.81 

27.41 

41.69 

27.60 

41.57 

27.78 

50 

«J 

o 

c; 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

6 

o 

a 

•w 

:o 

• P-4 

Q 

57 Deg. 

56| Deg. 

56$ Deg. 

56$ Deg. 

c 
c $ 

i n 

• PH 

Q 



















































































TRAVERSE TABLE 


69 


1; Distance. 

»- 

33 Deg. 

33* Deg. 

33* Deg. 

i 

33| Deg. 

Distance. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

51 

42.77 

27.78 

42.65 

27.96 

42.53 

28.15 

42.40 

28.33 

51 

52 

43.61 

28.32 

43.49 

28.51 

43.36 

28.70 

43.24 

28.89 

52 

53 

44.45 

28.87 

44.32 

29.06 

44.20 

29.25 

44.07 

29.45 

53 

54 

45.29 

29.41 

45.16 

29.61 

45.03 

29.80 

44.90 

30.00 

54 

55 

46.13 

29.96 

46.00 

30.16 

45.86 

30.36 

45.73 

30.56 

55 

56 

46.97 

30.50 

46.83 

30.70 

46.70 

30.91 

46.56 

31.11 

56 

57 

47.80 

31.04 

47.67 

31.25 

47.53 

31.46 

47.39 

31.67 

57 

58 

48.64 

31.59 

48.50 

31.80 

48.37 

32.01 

48.23 

32.22 

58 

59 

49.48 

32.13 

49.34 

32.35 

49.20 

32.56 

49.06 

32.78 

59 

60 

50.32 

32.68 

50.18 

32.90 

50.03 

33.12 

49.89 

33.33 

60 

61 

51.16 

33.22 

51.01 

33.45 

50.87 

33.67 

50.72 

33.89 

61 

62 

52.00 

33.77 

51.85 

33.99 

51.70 

34.22 

51.55 

34.45 . 

62 

63 

52.84 

34.31 

52.69 

34.54 

52.53 

34.77 

52.38 

35.00 

63 

64 

53.67 

34.86 

53.52 

35.09 

53.37 

35.32 

53.21 

35.56 

64 

65 

54.51 

35.40 

54.36 

35.64 

54.20 

35.88 

54.05 

36.11 

65 

66 

65.35 

35.95 

55.19 

36.19 

55.04 

36.43 

54.88 

36.67 

66 

67 

56.19 

36.49 

56.03 

36.74 

55.87 

36.98 

55.71 

37.22 

67 

68 

57.03 

37.04 

56.87 

37.28 

56.70 

37.53 

56.54 

37.78 

68 

69 

57.87 

37.58 

57.70 

37.83 

57.54 

38.08 

57.37 

38.33 

69 

70 

58.71 

38.12 

58.54 

38.38 

58.37 

38.64 

58.20 

38.89 

70 

71 

59.55 

38.67 

59.38 

38.93 

59.21 

39.19 

59.03 

39.45 

71 

72 

60.38 

39.21 

60.21 

39.48 

60.04 

39.74 

59.87 

40.00 

72 

73 

61.22 

39.76 

61.05 

40.03 

60.87 

40.29 

60.70 

40.56 

73 

74 

62.06 

40.30 

61.89 

40.57 

61.71 

40.84 

61.53 

41.11 

74 

75 

62.90 

40.85 

62.72 

41.12 

62.54 

41.40 

62.36 

41.67 

75 

76 

63.74 

41.39 

63.56 

41.67 

63.38 

41.95 

63.19 

42,22 

76 

77 

64.58 

41.94 

64.39 

42.22 

64.21 

42.50 

64.02 

42.78 

77 

78 

65.42 

42.48 

65.23 

42.77 

65.04 

43.05 

64.85 

43.33 

78. 

79 

66.25 

43.03 

66.07 

43.32 

65.88 

43.60 

65.69 

43.89 

79 

80 

67.09 

43.57 

66.90 

43.86 

66.71 

44.15 

66.52 

44.45 

80 

81 

67.93 

44.12 

67.74 

44.41 

67.54 

44.71 

67.35 

45.00 

81 

82 

68.77 

44.66 

68.58 

44.96 

68.38 

45.26 

68.18 

45.56 

82 

83 

69.61 

45.20 

69.41 

45.51 

69.21 

45.81 

69.01 

46.11 

83 

84 

70.45 

45.7 5 

70.25 

46.06 

70.05 

46.36 

69.84 

46.67 

84 

85 

71.29 

46.29 

71.08 

46.60 

70.88 

46.91 

70.67 

47.22 

85 

86 

72.13 

46.84 

71.92 

47.15 

71.71 

47.47 

71.51 

47.78 

86 

87 

72.96 

47.38 

72.76 

47.70 

72.55 

48.02 

72.34 

48.33 

87 

88 

73.80 

47.93 

73.59 

48.25 

73.38 

48.57 

73.17 

48.89 

88 

89 

74.64 

48.47 

74.43 

48.80 

74.22 

49.12 

74.00 

49.45 

89 

90 

75.48 

49.02 

75.27 

49.35 

75.05 

49.67 

74.83 

50.00 

90 

91 

76.32 

49.56 

76.10 

49.89 

75.88 

50.23 

75.66 

50.56 

91 

92 

77.16 

50.11 

76.94 

50.44 

76.72 

50.78 

76.50 

51.11 

92 

93 

78.00 

50.65 

77.77 

50.99 

77.55 

51.33 

77.33 

51.67 

93 

94 

78.83 

51.20 

73.61 

51.54 

78.39 

51.88 

78.16 

52.22 

94 

95 

79.67 

51.74 

79.45 

52.09 

79.22 

52.43 

78.99 

52.78 

95 

96 

80.51 

52.29 

80.28 

52.64 

80.05 

52.99 

79.82 

53.33 

96 

97 

81.35 

52.83 

81.12 

53.18 

80.89 

53.54 

80.65 

53.89 

97 

98 

82.19 

53.37 

81.96 

53.73 

81.72 

54.09 

81.48 

54.45 

98 

99 

83.03 

53.92 

82.79 

54.28 

82.55 

54.64 

82.32 

55.00 

99 

100 

83-87 

54.46 

83.63 

54.83 

83.39 

55.19 

1 

83.15 

55.56 

100 

6 

V 

Dep. 1 

Lat. 

Dep. 1 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

« 

o 

a 

S3 

ct 

-4-> 

r/j 

q 

57 Deg. 

56| Deg. 

56* Deg. 

56* Deg. 

a 

-*-> 

CO 

• 

Q 








































































































70 


TRAVERSE TABLE 


o 

M3* 

r-t> 

P 

34 Deg. 

34} Deg. 

34} Deg. 

34| Deg. 

0 
k- • 

M> 

!“*- 

P 

S3 

O 

(B 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

o 

? 

1 

0.83 

0.56 

0.83 

0.56 

0.82 

0.57 

0.82 

0.57 

1 

2 

1.66 

1.12 

1.65 

1.13 

1.65 

1.13 

1.64 

1.14 

2 

3 

2.49 

1.68 

2.48 

1.69 

2.47 

1.70 

2.46 

1.71 

3 

4 

3.32 

2.24 

3.31 

2.25 

3.30 

2.27 

3.29 

2.28 

4 

5 

4.15 

2.80 

4.13 

2.81 

4.12 

2.83 

4.11 

2.85 

5 

6 

4.97 

3.36 

4.96 

3.38 

4.94 

3.40 

4.93 

3.42 

6 

7 

5.80 

3.91 

5.79 

3.94 

5.77 

3.96 

5.75 

3.99 

7 

8 

6.63 

4.47 

6.61 

4.5Q 

6.59 

4.53 

6.57 

4.56 

8 

9 

7.46 

5.03 

7.44 

5.07 

7.42 

5.10 

7.39 

5.13 

9 

10 

8.29 

5.59 

8.27 

5.63 

8.24 

5.66 

8.22 

5.70 

10 

11 

9.12 

6.15 

9.09 

6.19 

9.07 

6.23 

9.04 

6.27 

11 

12 

9.95 

6.71 

9.92 

6.75 

9.89 

6.80 

9.86 

6.84 

12 

13 

10.78 

7.27 

10.75 

7.32 

10.71 

7.36 

10.68 

7.41 

13 

14 

11.61 

7.83 

11.57 

7.88 

11.54 

7.93 

11.50 

7.98 

14 

15 

12.44 

8.39 

12.40 

8.44 

12.36 

8.50 

12.32 

8.55 

15 

16 

13.26 

8.95 

13.23 

9.00 

13.19 

9.06 

13.15 

9.12 

16 

17 

14.09 

9.51 

14.05 

9.57 

14.01 

9.63 

13.97 

9.69 

17 

18 

14.92 

10.07 

14.88 

10.13 

14.83 

10.20 

14.79 

10.26 

18 

19 

15.75 

10.62 

15.71 

10.69 

15.66 

10.76 

15.61 

10.83 

19 

20 

16.58 

11.18 

16.53 

11.26 

16.48 

11.33 

16.43 

11.40 

20 

21 

17.41 

11.74 

17.36 

11.82 

17.31 

11.89 

17.25 

11.97 

21 

22 

18.24 

12.30 

18.18 

12.38 

18.13 

12.46 

18.08 

12.54 

22 

23 

19.07 

12.86 

19.01 

12.94 

18.95 

13.03 

18.90 

13.11 

23 

24 

19.90 

13.42 

19.84 

13.51 

19.78 

13.59 

19.72 

13.68 

24 

25 

20.73 

13.98 

20.66 

14.07 

20.60 

14.16 

20.54 

14.25 

25 

26 

21.55 

14.54 

21.49 

14.63 

21.43 

14.73 

21.36 

14.82 

26 

27 

22.38 

15.10 

22.32 

15.20 

22.25 

15.29 

22.18 

15.39 

27 

28 

23.21 

15.66 

23.14 

15.76 

23.08 

15.86 

23.01 

15.96 

28 

29 

24.04 

16.22 

23.97 

16.32 

23.90 

16.43 

23.83 

16.53 

29 

30 

24.87 

16.78 

24.80 

16.88 

24.72 

16.99 

24.65 

17.10 

30 

31 

25.70 

17.33 

25.62 

17.45 

25.55 

17.56 

25.47 

17.67 

31 

32 

26.53 

17.89 

26.45 

18.01 

26.37 

18.12 

26.29 

18.24 

32 

33 

27.36 

18.45 

27.28 

18.57 

27.20 

18.69 

27.11 

18.81 

33 

34 

28.19 

19.01 

28.10 

19.14 

28.02 

19.26 

27.94 

19.38 

34 

35 

29.02 

19.57 

28.93 

19.70 

28.84 

19.82 

28.76 

19.95 

35 

36 

29.85 

20.13 

29.76 

20.26 

29.67 

20.39 

29.58 

20.52 

36 

37 

30.67 

20.69 

30.58 

20.82 

30.49 

20.96 

30.40 

21.09 

37 

38 

31.50 

21.25 

31.41 

21.39 

31.32 

21.52 

31.22 

21.66 

38 

39 

32.33 

21.81 

32.24 

21.95 

32.14 

22.09 

32.04 

22.23 

39 

40 

33.16 

22.37 

33.06 

22.51 

32.97 

22.66 

32.87 

22.80 

40 

41 

33.99 

22.93 

33.89 

23.07 

33.79 

23.22 

33.69 

23.37 

41 

42 

34.82 

23.49 

34.72 

23.64 

34.61 

23.79 

34.51 

23.94 

42 

43 

35.65 

24.05 

35.54 

24.20 

35.44 

24.36 

35.33 

24.51 

43 

44 

36.48 

24.60 

36.37 

24.76 

36.26 

24.92 

36.15 

25.08 

44 

45 

37.31 

25.16 

37.20 

25.33 

37.09 

25.49 

36.97 

25.65 

45 

46 

38.14 

25.72 

38.02 

25.89 

37.91 

26.05 

37.80 

26.22 

46 

47 

38.96 

26.28 

38.85 

26.45 

38.73 

26.62 

38.62 

26.79 

47 

48 

39.79 

26.84 

39.68 

27.01 

39.56 

27.19 

39.44 

27.36 

48 

49 

40.62 

27.40 

40.50 

27.58 

40.38 

27.75 

40.26 

27.93 

49 

50 

41.45 

27.96 

41.33 

28.14 

41.21 

28.32 

41.08 

28.50 

50 

6 

o 

Dep. j 

Lat. 

Dep. 

Lat. 

Dep. i 

Lat. 

Dep. 

Lat. 

<u 

o 

■+-> 

Cf) 

Q 

56 Deg. 

55| Deg. 

55} Deg. 

55} Deg. 

a 

tn 

S 

. 






































































TRAVERSE TABLE, 


71 


J 


o 
'. 

m 

r-t* 

p 

*3 

34 Deg. 

344 Deg. 

34£ Deg. 

34* Deg. 

C 
**• 
w 
r** 

P 

o 

(6 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

S3 

O 

(5 

51 

42.28 

28.52 

42.16 

28.70 

42.03 

W ' 

28.89 

41.90 

29.07 

51 

52 

43.11 

29.08 

42.98 

29.27 

42.85 

29.45 

42.73 

29.64 

52 

53 

43.94 

29.64 

43.81 

29.83 

43.68 

30.02 

43.55 

30.21 

53 

54 

44.77 

30.20 

44.64 

30.39 

44.50 

30.59 

44.37 

30.78 

54 

55 

45*60 

30.76 

45.46 

30.95 

45.33 

31.15 

45.19 

31.35 

55 

; 56 

46.43 

31.31 

46.29 

31.52 

46.15 

31.72 

46.01 

31.92 

56 

57 

47.26 

31.87 

47.12 

32.08 

46.98 

32.29 

46.83 

32.49 

57 

58 

48.08 

32.43 

47.94 

32.64 

47.80 

32.85 

47.66 

33.06 

58 

59 

48.91 

32.99 

48.77 

33.21 

48.62 

33.42 

48.48 

33.63 

59 

60 

49*74 

33.55 

49.60 

33.77 

49.45 

33.98 

49.30 

34.20 

60 

61 

50.57 

34.11 

50.42 

34.33 

50.27 

34.55 

50.12 

34.77 

61 

62 

51.40 

34.67 

51.25 

34.89 

51.10 

35.12 

50.94 

35.34 

62 

63 

52.23 

35.23 

52.08 

35.46 

51.92 

35.68 

51.76 

35.91 

63 

64 

53*06 

35.79 

52.90 

36.02 

52.74 

36.25 

52.59 

36.48 

64 

65 

53.89 

36.35 

53.73 

36.58 

53.57 

36.82 

53.41 

37.05 

65 

66 

54.72 

36.91 

54*55 

37.15 

54.39 

37.38 

54.23 

37.62 

66 

67 

55.55 

37.46 

55.38 

37.71 

55.22 

37.95 

55.05 

38.19 

67 

68 

56.37 

38.03 

56.21 

38.27 

56.04 

38.52 

55.87 

38.76 

68 

69 

57.20 

38.58 

57.03 

38.83 

56.86 

39.08 

56.69 

39.33 

69 

70 

58.03 

39.14 

57.86 

39.40 

57.69 

39.65 

57.52 

39.90 

70 

71 

58.86 

39.70 

58.69 

39.96 

58.51 

40.21 

58.34 

40.47 

71 

72 

59.69 

40.26 

59.51 

40.52 

59.34 

40.78 

59.16 

41.04 

72 

73 

60.52 

40.82 

60.34 

41.08 

60.16 

41.35 

59.98 

41.61 

73 

74 

61*35 

41.38 

61.17 

41.65 

60.99 

41.91 

60.80 

42.18 

74 

75 

62.18 

41.94 

61.99 

42.21 

61.81 

42.48 

61.62 

42.75 

75 

76 

63.01 

42.50 

62.82 

42.77 

62.63 

43.05 

62.45 

43.32 

76 

77 

63.84 

43.06 

63.65 

43.34 

63.46 

43.61 

63.27 

43.89 

77 

78 

64.66 

43.62 

64.47 

43.90 

64.28 

44.18 

64.09 

44.46 

78 

79 

65.49 

44.18 

65.30 

44.46 

65.11 

44.75 

64.91 

45.03 

79 

80 

66.32 

44.74 

66.13 

45.02 

65.93 

45.31 

65.73 

45.60 

80 

81 

67.15 

45.29 

66.95 

45.59 

66.75 

45.88 

66.55 

46.17 

81 

82' 

67.98 

45.85 

67.78 

46.15 

67.58 

46.45 

67.37 

46.74 

82 

83 

68.81 

46.41 

68.61 

46.71 

68.40 

47.01 

68.20 

47.31 

83 

84 

69.64 

46.97 

69.43 

47.28 

69.23 

47.58 

69.02 

47.88 

84 

85 

70.47 

47.53 

70; 26 

47.84 

70.05 

48.14 

69.84 

48.45 

85 

86 

71.30 

48.09 

71.09 

48.40 

7ft. 87 

48.71 

70.66 

49.02 

86 

87 

72.13 

48.65 

71.91 

48.96 

71.70 

49.28 

71.48 

49.59 

87 

88 

72.96 

49.21 

72.74 

49.53 

72.52 

49.84 

72.30 

50.16 

88 

89 

73.78 

49.77 

73.57 

50.09 

73.35 

50.41 

73.13 

50.73 

89 

90 

74.61 

50; 33 

74.39 

50.65 

74.17 

50.98 

73.95 

51.30 

90 

91 

75.44 

50.89 

75.22 

51.22 

75.00 

51.54 

74.77 

51.87 

91 

92 

76.27 

51.45 

76.05 

51.78 

75.82 

52.11 

75.59 

52.44 

92 

93 

77.10 

52.00 

76.87 

52.34 

76.64 

52.68 

76.41 

53.01 

93 

94 

77.93 

52.56 

77; 70 

52.90 

77.47 

53.24 

77.23 

53.58 

94 

95 

78.76 

53.12 

78.53 

53.47 

78.29 

53.81 

78.06 

54.15 

95 

96 

79.59 

53.68 

79.35 

54.03 

79.12 

54.37 

78.88 

54.72 

96 

97 

80.42 

54.24 

80.18 

54.59 

79.94 

54.94 

79.70 

55.29 

97 

98 

81.25 

54.80 

81.01 

55.15 

80.76 

55.51 

80.52 

55.86 

98 

99 

82.07 

55.36 

81.83 

55.72 

81.59 

56.07 

81.34 

56.43 

99 

100 

82.90 

55.92 

82.66 

56.28 

82.41 

56.64 

82.16 

57.00 

100 

a; 

o 

Dep. 

Lat. 

Dep. 

1 

Lat. 

Dep. I 

Lat. 

Dep. J 

Lat. 

• 

0) 

0 

d 

-+-j 

Vi 

• H 

Q 

56 Deg. 

55| Deg. 

55 £ Deg. 

55* Deg. 

- 4 -* 

c n 

s 











































































































72 


TRAVERSE TABLE 


I 2 

rn 

ff 

P 

35 Deg. 

35$ Deg. 

35$ Deg. 

35$ Deg. 

C 

in 

rt> 

P 

s 

0 

o 

to 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

o 

to 

1 

0.82 

0.57 

0.82 

0.58 

0.81 

0.58 

0.81 

0.58 

1 

2 

1.64 

1.15 

1.63 

1.15 

1.63 

1.16 

1.62 

1.17 

2 

3 

2.46 

1.72 

2.45 

1.73 

2.44 

1.74 

2.43 

1.75 

3 

4 

3.28 

2.29 

3.27 

2.31 j 

3.26 

2.32 

3.25 

2.34 

4 

5 

4.10 

2.87 

4.08 

2.89 

4.07 

2.90 

4.06 

2.92 

5 

6 

4.91 

3.44 

4.90 

3.46 | 

4.88 

3.48 

4.87 

3.51 

6 

7 

5.73 

4.01 

5.72 

4.04 j 

5.70 

4.06 

5.68 

4.09 

7 

8 

6.55 

4.59 

6.53 

4.62 [ 

^>51 

4.65 

6.49 

4.67 

8 

9 

7.37 

5.16 

7.35 

5.19 

7.33 

5.23 

7.30 

5.26 

9 

10 

8.19 

5.74 

8.17 

5.77 I 

- i 

8.14 

5.81 

8.12 

5.84 

10 

11 

9.01 

6.31 

8.98 

6.35 

8.96 

6.39 

8.93 

6.43 

11 

12 

9.83 

6.88 

9.80 

6.93 

9.77 

6.97 

9.74 

7.01 

12 

13 

10.65 

7.46 

10.62 

7.50 , 

10.58 

7.55 

10.55 

7.60 

13 

14 

11.47 

8.03 

11.43 

8.08 j 

11.40 

8.13 

11.36 

8.18 

14 

15 

12.29 

8.60 

12.25 

8.66 : 

12.21 

8.71 

12.17 

8.76 

15 

16 

13.11 

9.18 

13.07 

9.23 

13.03 

9.29 

12.99 

9.35 

16 

17 

13.93 

9.75 

13.88 

9.81 

13.84 

9.87 

13.80 

9.93 

17 

18 

14.74 

10.32 

14.70 

10.39 

14.65 

10.45 1 

14.61 

10.52 

18 

19 

15.56 

10.90 

15.52 

10.97 

15.47 

11.03 

15.42 

11.10 

19 

20 

16.38 

11.47 

16.33 

11.54 

16.28 

11.61 

16.23 

11.68 

20 

21 

17.20 

12.05 

17.15 

12.12 j 

17.10 

12.19 

17.04 

12.27 

21 

22 

18.02 

12.62 

17.97 

12.70 j 

17.91 

12.78 

17.85 

12.85 

22 

23 

18.84 

13.19 

18.78 

13.27 

18.72 

13.36 

18.67 

13.44 

23 

24 

19.66 

13.77 

19.60 

13.85 

19.54 

13.94 

19.48 

14.02 

24 

25 

20.48 

14.34 

20.42 

14.43 ! 

20.35 

14.52 

20.29 

14.61 

25 

26 

21.30 

14.91 

21.23 

15.01 

21.17 

15.10 

21.10 

15.19 

26 

27 

22.12 

15.49 

22.05 

15.58 

21.98 

15.68 

21.91 

15.77 

27 

28 

22.94 

16.06 

22.87 

16.16 

22.80 

16.26 

22.72 

16.36 

28 

29 

23.76 

16.63 

23.68 

16.74 

23.61 

16.84 

23.54 

16.94 

29 

30 

24.57 

17.21 

24.50 

17.31 

24.42 

17.42 

24.35 

17.53 

30 

31 

25.39 

17.78 

25.32 

17.89 

25.24 

18.00 

25.16 

18.11 

31 

32 

26.21 

18.35 

26.13 

18.47 

26.05 

18.58 

25.97 

18.70 

32 

33 

27.03 

18.93 

26.95 

19.05 

26.87 

19.16 

26.78 

19.28 

33 

34 

27.85 

19.50 

27.77 

19.62 

27.68 

19.74 

27.59 

19.86 

34 

35 

28.67 

20.08 

28.58 

20.20 

28.49 

20.32 

28.41 

20.45 

35 

36 

29.49 

20.65 

29.40 

20.78 

29.31 

20.91 

29.22 

21.03 

36 

37 

30.31 

21.22 

30.22 

21.35 

30.12 

21.49 

30.03 

21.62 

37 

38 

31.13 

21.80 

31.03 

21.93 

! 30.94 

22.07 

30.84 

22.20 

38 

39 

31.95 

22.37 

31.85 

22.51 

! 31.75 

22.65 

31.65 

22.79 

39 

40 

32.77 

22.94 

32.67 

23.09 

j 32.56 

23.23 

32.46 

23.37 

40 

41 

33.59 

23.52 

33.48 

23.66 

\ 

i 33.38 

23.81 

33.27 

23.95 

41 

42 

34.40 

24.09 

34.30 

24.24 

{ 34.19 
|| 35.01 

24.39 

34.09 

24.54 

42 

43 

35.22 

24.66 

35.12- 

24.82 

24.97 

34.90 

25.12 

43 

44 

36.04 

25.24 

35.93 

25.39 

i 35.82 

25.55 

35.71 

25.71 

44 

45 

36.86 

25.81 

36.75 

25.97 

i 36.64 

26.13 

36.52 

26.29 

45 

46 

37.68 

26.38 

37.57 

26.55 

j 37.45 

26.71 

37.33 

26.88 

46 

47 

38.50 

26.96 

38.38 

27.13 

| 38.26 

27.29 

38.14 

27.46 

47 

48 

39.32 

27.53 

39.20 

27.70 

39.08 

27.87 

38.96 

28.04 

48 

49 

40.14 

28.11 

1 40.02 

28.28 

j 39.89 

28.45 

39.77 

28.63 

49 

50 

40.96 

28.68 

40.83 

28.86 

40.71 

L 

29.04 

40.58 

29.21 

50 

6 

o 

a 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

i 

Lat. 

Dep. 

Lat. 

« 

o 

CS 

CO 

• 

Q 

55 Deg. 

54f Deg. 

54$ Deg. 

1 

54$ Deg. 

1 

ct3 
w 
c n 

• ’"i 

Q 


\ 






































































































TRAVERSE TABLE. 73 


1 0 

■ >—' • 

V U3 

1 & 

S3 

1 <33 

1 » 

G * 

35 

Deg. 

35$ Deg. 

35$ Deg. 

351 Deg. 

G 
►— • 
u 

e 
>—< 

O 

O 

• 

Lat. 

Dep. 

Lat. 

| Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

1 51 

41.78 

29.25 

41.65 

29.43 

41.52 

29.62 

41.39 

29.80 

51 

52 

42.60 

29.83 

42.47 

30.01 

42.33 

30.20 

42.20 

30.38 

52 

| 53 

43.42 

30.40 

43.28 

30.59 

43.15 

30.78 

43.01 

30.97 

53 

l 54 

44.23 

30.97 

44.10 

31.17 

43.96 

31.36 

43.82 

31.55 

54 

j 55 

45.05 

31.55 

44.92 

31.74 

44.78 

31.94 

44.64 

32.13 

55 

56 

45.87 

32.12 

45.73 

32.32 

45.59 

32.52 

45.45 

32.72 

56 

57 

46.69 

32.69 

46.55 

32.90 

46.40 

33.10 

46.26 

33.30 

57 

I 58 

47.51 

33.27 

47.37 

33.47 

47.22 

33.68 

47.07 

33.89 

58 

59 

48.33 

33.84 

48.18 

34.05 

48.03 

34.26 

47.88 

34.47 

59 

60 

49.15 

34.41 

49.00 

34.63 

48.85 

34.84 

48.69 

35.05 

60 

I 61 

49.97 

34.99 

49.82 

35.21 

49.66 

35.42 

49.51 

35.64 

61 

: 62 

50.79 

35.56 

50.63 

35.78 

50.48 

36.00 

50.32 

36.22 

62 

63' 

51.61 

36.14 

51.45 

36.36 

51.29 

36.58 

51.13 

36.81 

63 

64 

52.43 

36.71 

52.27 

36.94 

52.10 

37.16 

51.94 

37.39 

64 

: j 65 

53.24 

37.28 

53.08 

37.51 

52.92 

37.75 

52.75 

37.98 

65 

I 66 

54.06 

37.86 

53.90 

38.09 

53.73 

38.33 

53.56 

<38.56 

66 

| 67 

54.88 

38.43 

54.71 

38.67 

54.55 

38.91 

54.38 

39.14 

67 

I 68 

55.70 

39.00 

55.53 

39.25 

55.36 

39.49 

55.19 

39.73 

68 

69 

56.52 

39.58 

56.35 

39.82 

56.17 

40.07 

56.00 

40.31 

69 

I 70 

57.34 

40.15 

57.16 

40.40 

56.99 

40.65 

56.81 

40.90 

70 

71 

58.16 

40.72 

57.98 

40.98 

57.80 

41.23 

57.62 

41.48 

71 

1 72 

58.98 

41.30 

58.80 

41.55 

58.62 

41.81 

58.43 

42.07 

72 

73 

59.80 

41.87 

59.61 

42.13 

59.43 

42.39 

59.24 

42.65 

73 

1 74 

60.62 

42.44 

60.43 

42.71 

60.24 

42.97 

60.06 

43.23 

74 

| 75 

61.44 

43.02 

61.25 

43.29 

61.06 

43.55 

60.87 

43.82 

75 

| 76 

62.26 

43.59 

62.06 

43.86 

61.87 

44.13 

61.68 

44.40 

75 

77 

63.07 

44.17 

62.88 

44.44 

62.69 

44.71 

62.49 

44.99 

77 

; 78 

63.89 

44.74 

63.70 

45.02 

63.50 

45.29 

63.30 

.45.57 

78 

I 79 

64.71 

45.31 

64.51 

45.59 

64.32 

45.88 

64.11 

46.16 

79 

: 80 

65.53 

45.89 

65.33 

46.17 

65.13 

46.46 

64.93 

46.74 

80 

1 81 

66.35 

46.46 

66.15 

46.75 

65.94 

47.04 

65.74 

47.32 

81 

1 82 

67.17 

47.03 

66.96 

47.33 

66.76 

47.62 

66.55 

47.91 

82 

I 83 

67.99 

47.61 

67.78 

47.90 

67.57 

48.20 

67.36 

48.49 

83 

I 84 

68.81 

48.18 

68.60 

48.48 

68.39 

48.78 

68.17 

49.08 

84 

I 85 

69.63 

48.75 

69.41 

49.06 

69.20 

49.36 

68.98 

49.66 

85 

E 86 

70.45 

49.33 

70.23 

49.63 

70.01 

49.94 

69.80 

50.25 

86 

fi 87 

71.27 

49.90 

71.05 

50.21 

70.83 

50.52 

70.61 

50.83 

87 

I 88 

72.09 

50.47 

71.86 

50.79 

71.64 

51.10 

71.42 

51.41 

88 

1 ! 89 

72.90 

51.05 

72.68 

51.37 

72.46 

51.68 

72.23 

52.00 

89 

j 90 

73.72 

51.62 

73.50 

51.94 

73.27 

52.26 

73.04 

52.58 

90 

| 91 

74.54 

52.20 

74.31 

52.52 

74.08 

52.84 • 

73.85 

53.17 

91 

I 92 

75.36 

52.77 

75.13 

53.10 

74.90 

53.42 

74.66 

53.75 

92 . 

| 93 

76.18 

53.34 

75.95 

53.67 

75.71 

54.01 

75.48 

54.34 

93 

1 94 

77.00 

53.92 

76.76 

54.25 

76.53 

54.59 

76.29 

54.92 

94 

r 95 

77.82 

54.49 

77.58 

54.83 

77.34 

55.17 

77.10 

55.50 

95 

1 96 

78.64 

55.06 

78.40 

55.41 

78.16 

55.75 

77.91 

56.09 

96 

1 97 

79.46 

55.64 

79.21 

55.98 

78.97 

56.33 

78.72 

56.67 

97 

98 

80.28 

56.21 

80.03 

56.56 

79.78 

56.91 

79.53 

57.26 

98 

I 99 

81.10 

56.78 

80.85 

57.14 

80.60 

57.49 

80.35 

57.84 

99 

||100 

81-92 

57.36 

81.66 

57.71 

81.41- 

58.07 

81.16 

58-42 

100 

i V 

II 0 

Dep. 1 

Lat. j 

Dep. 

Lat. 

Dep. 

Lat. j 

Dep. 

Lat. 

8 

a 

I C 

II ^ 

■ I m 

II * 

| a 

55 Deg. | 

54$ Dag. 

54$ Deg. 

54$ Deg. 

_ 

at 

• 

3 


K 


















































































































74- 


TRAVERSE TABLE 


G 

*--• 

w 

r-*- 

P 

36 Deg. 

36i Deg. 

1 

36 i Deg. 

36J Deg. 

O 

in 

r~+- 

P 

cs 

o 

(6 

Lat. 

Dep. 

Lat. 

Dep. | 

Lat. 

Dep. 

Lat. 

Dep. 

o 

n 

1 

0.81 

0.59 

0.81 

0.59 

0.80 

0.59 

0.80 

0.60 

1 

2 

1.62 

1.18 

1.61 

1.18 

1.61 

1.19 

1.60 

1.20 

2 

3 

2.43 

1.76 

2.42 

1.77 

2.41 

1.78 

2.40 

1.79 

3 

4 

3.24 

2.35 

3.23 

2.37 

3.22 

2.38 

3.20 

2.39 

4 

5 

4.05 

2.94 

4.03 

2.96 

4.02 

2.97 

4.01 

2.99 

5 

6 

4.85 

3.53 

4.84 

3.55 

4.82 

3.57 

4.81 

3.59 

6 

7 

5.66 

4.11 

5.65 

4.14 

5.63 

4.16 

5.61 

4.19 

7 

8 

6.47 

4.70 

6.45 

4.73 

6.43 

4.76 

6.41 

4.79 

8 

9 

7.28 

5.29 

7.26 

5.32 

7.23 

5.35 

7.21 

5.38 

9 

10 

8.09 

5.88 

8.06 

5.91 

8.04 

5.95 

8.01 

5.98 

10 

11 

8.90 

6.47 

8.87 

6.50 

8.84 

6.54 

8.81 

6.58 

11 

12 

9.71 

7.05 

9.68 

7.10 

9.65 

7.14 

9.61 

7.18 

12 

13 

10.52 

7.64 

10.48 

7.69 

10.45 

7.73 

10.42 

7.78 

13 

14 

11.33 

8.23 

11.29 

8.28 

11.25 

8.33 

11.22 

8.38 

14 

15 

12.14 

8.82 

12.10 

8.87 

12.06 

8.92 

12.02 

8.97 

15 

16 

12.94 

9.40 

12.90 

9.46 

12.86 

9.52 

12.82 

9.57 

16 

17 

13.75 

9.99 

13.71 

10.05 

13.67 

10.11 

13.62 

10.17 

17 

18 

14.56 

10.58 

14.52 

10.64 

14.47 

10.71 

14.42 

10.77 

18 

19 

15.37 

11.17 

15.32 

11.23 1 

15.27 

11.30 

15.22 

11.37 

19 

20 

16.18 

11.76 

16.13 

11.83 

16.08 

11.90 

16.03 

11.97 

20 

21 

16.99 

12.34 

16.94 

12.42 

16.88 

12.49 

16.83 

12.56 

21 

22 

17.80 

12.93 

17.74 

13.01 

17.68 

13.09 

17.63 

13.16 

22 

23 

18.61 

13.52 

18.55 

13.60 

18.49 

13.68 

18.43 

13.76 

23 

24 

19.42 

14.11 

19.35 

14.19 

19.29 

14.28 

19.23 

14.36 

24 

25 

20.23 

14.69 

20.16 

14.78 

20.10 

14.87 

20.03 

14.96 

25 

26 

21.03 

15.28 

20.97 

15.37 

20.90 

15.47 

20.83 

15.56 

26 

27 

21.84 

15.87 

21.77 

15.97 

21.70 

16.06 

21.63 

16.15 

27 

28 

22.65 

16.46 

22.58 

16.56 

22.51 

16.65 

22.44 

16.75 

28 

29 

23.46 

17.05 

23.39 

17.15 

23.31 

17.25 

23.24 

17.35 

29 

30 

24.27 

17.63 

24.19 

17.74 

24.12 

17.84 

24.04 

17.95 

30 

31 

25.08 

18.22 

25.00 

18.33 

24.92 

18.44 

24.84* 

18.55 

31 

32 

25.89 

18.81 

25.81 

18.92 

25.72 

19.03 

25.64 

19.15 

32 

33 

26.70 

19.40 

26.61 

19.51 

26.53 

19.63 

26.44 

19.74 

33 

34 

27.51 

19.98 

27.42 

20.10 

27.33 

20.22 

27.24 

20.34 

34 

35 

28.32 

20.57 

28.23 

20.70 

28.13 

20.82 

28.04 

20.94 

35 

36 

29.12 

21.16 

29.03 

21.29 

28.94 

21.41 

28.85 

21.54 

36 

37 

29.93 

21.75 

29.84 

21.88 

29.74 

22.01 

29.65 

22.14 

37 

38 

30.74 

22.34 

30.64 

22.47 

30.55 

22.60 

30.45 

22.74 

38 

39 

31.55 

22.92 

31.45 

23.06 

31.35 

23.20 

31.25 

23.33 

39 

40 

32.36 

23.51 

32.26 

23.65 

32.15 

23.79 

32.05 

23.93 

40 

41 

33.17 

24.10 

33.06 

24.24 

32.96 

24.39 

32.85 

24.53 

41 

42 

33.98 

24.69 

33.87 

24.83 

33.76 

24.98 

33.65 

25.13 

42 

43 

34.79 

25.27 

34.68 

25.43 

34.57 

25.58 

34.45 

25.73 

43 

44 

35.60 

25.86 

35.48 

26.02 

35.37 

26.17 

35.26 

26.33 

44 

45 

36.41 

26.45 

36.29 

26.61 

36.17 

26.77 

36.06 

26.92 

45 

46 

37.21 

27.04 

37.10 

27.20 

36.98 

27.36 

36.86 

27.52 

46 

47 

38.02 

27.63 

37.90 

27.79 

37.78 

27.96 

37.66 

2842 

47 

48 

38.83 

28.21 

38.71 

28.38 

38.59 

28.55 

38.46 

28.72 

48 

49 

39.64 

28.80 

39.52 

28.97 

39.39 

29.15 

39.26 

29.32 

49 

50 

40.45 

29.39 

40.32 

29.57 

40.19 

29.74 

40.06 

29.92 

50 

<u 

o 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

• 

0) 

o 

C5 

4-J 

if) 

• "H 

G 

54 

Deg. 

531 

1 

Deg. 

53* 

Deg. 

53* 

Deg. 

CT3 

<n 

• H 

Q 













































































































TRAVERSE TABLE. 

V 


o 

t— . 

OD 

r+ 

P 

J3 

36 Deg. 

36$ Deg. 

36 £ Deg. 

361 Deg. 

0 

M. 

W) 

P 

o 

re 

• 

Lat. 

Dep. 

Lat. j 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

13 

O 

re 

51 

41.26 

29.98 

41.13 

30.16 

41.00 

30.34 

40.86 

30.51 

51 

52 

42.07 

30.56 

41.94 

30.75 

41.80 

30.93 

41.67 

31.11 

52 

53 

42.88 

31.15 

42.74 

31.34 

42.60 

31.53 

42.47 

31.71 

53 

54 

43.69 

31.74 

43.55 

31.93 

43.41 

32.12 

43.27 

32.31 

54 

55 

44.50 

32.33 

44.35 

32.52 

44.21 

32.72 

44.07 

32.91 

55 

56 

45.30 

32.92 

45.16 

33.11 

45.02 

33.31 

44.87 

33.51 

56 

57 

46.11 

33.50 

45.97 

33.70 

45.82 

33.90 

45.67 

34.10 

57 

58 

46.92 

34.09 

46.77 

34.30 

46.62 

34.50 

46.47 

34.70 

58 

59 

47.73 

34.68 

47.58 

34.89 

47.43 

35.09 

47.27 

35.30 

59 

60 

48.54 

35.27 

48.39 

35.48 

48.23 

35.69 

48.08 

35.90 

60 

61 

49.35 

35.85 

49.19 

36.07 

49.04 

36.28 

48.88 

36.50 

61 

62 

50.16 

36.44 

50.00 

36.66 

49.84 

36.88 

49.68 

37.10 

62 

63 

50.97 

37.03 

50.81 

37.25 

50.64 

37.47 

50.48 

37.69 

63 

64 

51.78 

37.62 

51.61 

37.84 

51.45 

38.07 

51.28 

38.29 

64 

65 

52.59 

38.21 

52.42 

38.44 

52.25 

38.66 

52.08 

38.89 

65 

66 

53.40 

38.79 

53.23 

39.03 

53.05 

39.26 

52.88 

39.49 

66 

67 

54.20 

39.38 

54.03 

39.62 

53.86 

39.85 

53.68 

40.09 

67 

68 

55.01 

39.97 

54.84 

40.21 

54.66 

40.45 

54.49 

40.69 

68 

69 

55.82 

40.56 

55.64 

40.80 

55.47 

41.04 

55.29 

41.28 

69 

70 

56.63 

41.14 

56.45 

41.39 

56.27 

41.64 

56.09 

41.88 

70 

71 

57.44 

41.73 

57.26 

41.98 

57.07 

42.23 

56.89 

42.48 

71 

72 

58.25 

42.32 

58.06 

42.57 

57.88 

42.83 

57.69 

43.08 

72 

73 

59.06 

42.91 

58.87 

43.17 

58.68 

43.42 

58.49 

43.68 

73 

74 

59.87 

43.50 

59.68 

43.76 

59.49 

44.02 

59.29 

44.28 

74 

75 

60.68 

44.08 

60.48 

44.35 

60.29 

44.61 

60.09 

44.87 

75 

76 

61.49 

44.67 

61.29 

44.94 

61.09 

45.21 

60.90 

45.47 

76 

77 

62.29 

45.26 

62.10 

45.53 

61.90 

45.80 

61.70 

46.07 

77 

78 

63.10 

45.85 

62.90 

46.12 

62.70 

46.40 

62.50 

46.67 

78 

79 

63.91 

46.43 

63.71 

46.71 

63.50 

46.99 

63.30 

47.27 

79 

80 

64.72 

47.02 

64.52 

47.30 

64.31 

47.59 

64.10 

47.87 

80 

81 

65.53 

47.61 

65.32 

47.90 

65.11 

48.18 

64.90 

48.46 

81 

82 

66.34 

48.20 

66.13 

48.49 

65.92 

48.78 

65.70 

49.06 

82 

83 

67.15 

48.79 

66.93 

49.08 

66.72 

49.37 

66.50 

49.66 

83 

84 

67.96 

49.37 

67.74 

49.67 

67.52 

49.97 

67.31 

50.26 

84 

85 

68.77 

49.96 

68.55 

50.26 

68.33 

50.56 

68.11 

50.86 

85 

86 

69.58 

50.55 

69.35 

50.8 5 

69.13 

51.15 

68.91 

51.46 

86 

87 

70.38 

51.14 

70.16 

51.44 

69.94 

51.75 

69.71 

52.05 

87 

88 

71.19 

51.73 

70.97 

52.04 

70.74 

52.34 

70.51 

52.65 

88 

89 

72.00 

52.31 

71.77 

52.63 

71.54 

52.94 

71.31 

53.25 

89 

90 

72.81 

52.90 

72.58 

53.22 

72.35 

53.53 

72.11 

53.85 

90 

91 

73.62 

53.49 

73.39 

53.81 

73.15 

54.13 

72.91 

54.45 

91 

92 

74.43 

54.08 

74.19 

54.40 

73.95 

54.72 

73.72 

55.05 

92 

93 

75.24 

54.66 

75.00 

54.99 

74.76 

55.32 

74.52 

55.64 

93 

94 

76.05 

55.25 

75.81 

55.58 

75.56 

55.91 

75.32 

56.24 

94 

95 

76.86 

55.84 

76.61 

56.17 

76.37 

56.51 

76.12 

56.84 

95 

96 

77.67 

56.43 

77.42 

56.77 

77.17 

57.10 

76.92 

57.44 

96 

97 

78.47 

57.02 

78.23 

57.36 

77.97 

57.70 

77.72 

58.04 

97 

98 

79.28 

57.60 

79.03 

57.95 

78.78 

58.29 

78.52 

58.64 

98 

99 

80.09 

58.19 

79.84 

58.54 

79.58 

58.89 

79.32 

59.23 

99 

100 

80.90 

58.78 

80.64 

59.13 

80.39 

59.48 

80.13 

59.83 

100 

re 

o 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

re 

o 

p 

C 

ctJ 

r/J 

Q 

54 Deg. 

53J Deg. 

53$ Deg. 

53$ Deg. 

i 

CfJ 

5 























































































76 


TRAVERSE TABLE 


d 

r/j* 

f - ► 

P 

37 Deg. 

37$ Deg. 

37$ Deg. 

37| Deg. 

d 

IQ ’ 

r*- 

P 

£3 

O 

? 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

o 

• 

1 

0.80 

0.60 

0.80 

0.61 

0.79 

0.61 

0.79 

0.61 

1 

2 

1.60 

1.20 

1.59 

1.21 

1.59 

1.22 

1.58 

1.22 

2 

3 

2.40 

1.81 

2.39 

1.82 

2.38 

1.83 

2.37 

1.84 

3 

4 

3.19 

2.41 

3.18 

2.42 

3.17 

2.43 

3.16 

2.45 

4 

5 

3.99 

3.01 

3.98 

3.03 

3.97 

3.04 

3.95 

3.06 

5 

6 

4.79 

3.61 

4.78 

3.63 

4.76 

3.65 

4.74 

3.67 

6 

7 

5.59 

4.21 

5.57 

4.24 

5.55 

4.26 

5.53 

4.29 

7 

8 

6.39 

4.81 

6.37 

4.84 

6.35 

4.87 

6.33 

4.90 

8 

9 

7.19 

5.42 

7.16 

5.45 

7.14 

5.48 

7.12 

5.51 

9 

10 

7.99 

6.02 

7.96 

6.05 

7.93 

6.09 

7.91 

6.12 

10 

11 

8.78 

6.62 

8.76 

6.66 

8.73 

6.70 

8.70 

6.73 

11 

12 

9.58 

7.22 

9.55 

7.26 

9.52 

7.31 

9.49 

7.35 

12 

13 

10.38 

7.82 

10.35 

7.87 

10.31 

7.91 

10.28 

7.96 

13 

14 

11.18 

8.43 

11.14 

8.47 

11.11 

8.52 

11.07 

8.57 

14 

15 

11.98 

9.03 

11.94 

9.08 

11.90 

9.13 

11.86 

9.18 

15 

16 

12.78 

9.63 

12.74 

9.68 

12.69 

9.74 

12.65 

9.80 

16 

17 

13.58 

10.23 

13.53 

10.29 

13.49 

10.35 

13.44 

10.41 

17 

18 

14.38 

10.83 

14.33 

10.90 

14.28 

10.96 

14.23 

11.02 

18 

19 

15.17 

11.43 

15.12 

11.50 

15.07 

11.57 

15.02 

11.63 

19 

20 

15.. 97 

12.04 

15.92 

12.11 

15.87 

12.18 

15.81 

12.24 

20 

21 

16.77 

12.64 

16.72 

12.71 

16.66 

12.78 

16.60 

12.86 

21 

22 

17.57 

13.24 

17.51 

13.32 

17.45 

13.39 

17.40 

13.47 

22 

23 

18.37 

13.84 

18.31 

13.92 

18.25 

14.00 

18.19 

14.08 

23 

24 

19.17 

14.44 

19.10 

14.53 

19.04 

14.61 

18.98 

14.69 

24 

25 

19.97 

15.05 

19.90 

15.13 

19.83 

15.22 

19.77 

15.31 

25 

26 

20.76 

15.65 

20.70 

15.74 

20.63 

15.83 

20.56 

15.92 

26 

27 

21.56 

16.25 

21.49 

16.34 

21.42 

16.44 

21.35 

16.53 

27 

28 

22.36 

16.85 

22.29 

16.95 

22.21 

17.05 

22.14 

17.14 

28 

29 

23.16 

17.45 

23.08 

17.55 

23.01 

17.65 

22.93 

17.75 

29 

30 

23.96 

18.05 

23.88 

18.16 

23.80 

18.26 

23.72 

18.37 

30 

31 

24.76 

18.66 

24.68 

18.76 

24.59 

18.87 

24.51 

18.98 

31 

32 

25.56 

19.26 

25.47 

19.37 

25.39 

19.48 

25.30 

19.59 

32 

33 

26.35 

19.86 

26.27 

19.97 

26.18 

20.09 

26.09 

20.20 

33 

34 

27.15 

20.46 

27.06 

20.58 

26.97 

20.70 

26.88 

20.82 

34 

35 

27.95 

21.06 

27.86 

21.19 

27.77 

21.31 

27.67 

21.43 

35 

36 

28.75 

21.67 

28.66 

21.79 

28.56 

21.92 

28.46 

22.04 

36 

37 

29.55 

22.27 

29.45 

22.40 

29.35 

22.52 

29.26 

22.65 

37 

38 

30.35 

22.87 

30.25 

23.00 

30.15 

23.13 

30.05 

23.26 

38 

39 

31.15 

23.47 

31.04 

23.61 

30.94 

23.74 

30.84 

23.88 

39 

40 

31.95 

24.07 

31.84 

24.21 

31.73 

24.35 

31.63 

24.49 

40 

41 

32.74 

24.67 

32.64 

24.82 

32.53 

24.96 

32.42 

25.10 

41 

42 

33.54 

25.28 

33.43 

25.42 

33.32 

25.57 

33.21 

25.71 

42 

43 

34.34 

25.88 

34.23 

26.03 

34.11 

26.18 

34.00 

26.33 

43 

44 

35.14 

26.48 

35.02 

26.63 

34.91 

26.79 

34.79 

26.94 

44 

45 

35.94 

27.08 

35.82 

27.24 

35.70 

27.39 

35.58 

27.55 

45 

46 

36.74 

27.68 

36.62 

27.84 

36.49 

28.00 

36.37 

28.16 

46 

47 

37.54 

28.29 

37.41 

28.45 

37.29 

28.61 

37.16 

28.77 

47 

48 

38.33 

28.89 

38.21 

29.05 

38.08 

29.22 

37.95 

29.39 

48 

49 

39.13 

29.49 

39.00 

29.66 

38.87 

29.83 

38.74 

30.00 

49 

50 

39.93 

30.09 

39.80 

30.26 

39.67 

30.44 

39.53 

30.61 

50 

o 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

aJ 

o 

-w 

in 

53 Deg. 

52f Deg. 

62$ Deg. 

52$ Deg. 

r\ 

















































































TRAVERSE TABLE, 


77 


d 

DO* 

r-f- 

P 

37 Deg. 

i 

37 i 

Deg. 

37 i 

Deg. 

371 

Deg. 

d 
»-* . 

Ui 

r+ 

P 

o 

» 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

D 

O 

to 

• 

51 

40.73 

30.69 

40.60 

30.87 

40.46 

31.05 

40.33 

31.22 

51 

52 

41.53 

31.29 

41.39 

31.48 

41.25 

31.66 

41.12 

31.84 

52 

53 

42.33 

31.90 

42.19 

32.08 

42.05 

32.26 

41.91 

32.45 

53 

54 

43.13 

32.50 

42.98 

32.69 

42.84 

32.87 

42.70 

33.06 

54 

55 

43.92 

33.10 

43.78 

33.29 

43.63 

33.48 

43.49 

33.67 

55 

56 

44.72 

33.70 

44.58 

33.90 

44.43 

34.09 

44.28 

34.28 

56 

57 

45.52 

34.30 

45.37 

34.50 

45.22 

34.70 

45.07 

34.90 

57 

• 58 

46.32 

34.91 

46.17 

35.11 

46.01 

35.31 

45.86 

35.51 

58 

59 

47.12 

35.51 

46.96 

35.71 

46.81 

35.92 

46.65 

36.12 

59 

60 

47.92 

36.11 

47.76 

36.32 

47.60 

36.53 

47.44 

36.73 

60 

61 

48.72 

36.71 

48.56 

36.92 

48.39 

37.13 

48.23 

37.35 

61 

1 62 

49.52 

37.31 

j 49.35 

37.53 

49.19 

37.74 

49.02 

37.96 

62 

63 

50.31 

37.91 

1 50.15 

38.13 

49.98 

38.35 

49.81 

38.57 

63 

64 

51.11 

38.52 

i 50.94 

38.74 

50.77 

38.96 

50.60 

39.18 

64 

65 

51.91 

39.12 

51.74 

39.34 

51.57 

39.57 

51.39 

39.79 

65 

66 

52.71 

39.72 

52.54 

39.95 

52.36 

40.18 

52.19 

40.41 

66 

07 

53.51 

40.32 

53.33 

40.55 

53.15 

40.79 

52.98 

41.02 

67 

68 

54.31 

40.92 

54.13 

41.16 

53.95 

41.40 

53.77 

41.63 

68 

■ 69 

55.11 

41.53 

54.92 

41.77 

54.74 

42.00 

54.56 

42.24 

69 

v 70 

55.90 

42.13 

55.72 

42.37 

55.53 

42.61 

55.35 

42.86 

70 

71 

56.70 

42.73 

56.52 

42.98 

56.33 

43.22 

56.14 

43.47 

71 

i 72 

57.50 

43.33 

57.31 

43.58 

57.12 

43.83 

56.93 

44.08 

72 

73 

58.30 

43.93 

58.11 

44.19 

57.91 

44.44 

57.72 

44.69 

73 

! 74 

59.10 

44.53 

58.90 

44.79 

58.71 

45.05 

58.51 

45.30 

74 

75 

59.90 

45.14 

59.70 

45.40 

59.50 

45.66 

59.30 

45.92 

75 

76 

60.70 

45.74 

60.50 

46.00 

60.29 

46.27 

60.09 

46.53 

76 

77 

61.49 

46.34 

61.29 

46.61 

61.09 

46.87 

60.88 

47.14 

77 

78 

62.29 

46.94 

62.09 

47.21 

61.88 

47.48 

61.67 

47.75 

78 

79 

63.09 

47.54 

62.88 

47.82 

62.67 

48.09 

62.46 

48.37 

79 

80 

63.89 

48.15 

63.68 

48.42 

63.47 

48.70 

63.26 

4%. 98 

80 

81 

64.69 

48.75 

64.48 

49.03 

64.26 

49.31 

64.05 

49.59 

81 

82 

65.49 

49.35 

65.27 

49.63 

65.05 

49.92 

64.84 

50.20 

82 

83 

66.29 

49.95 

66.07 

50.24 

65.85 

50.53 

65.63 

50.81 

83 

84 

67.09 

50.55 

66.86 

50.84 

66.64 

51.14 

66.42 

51.43 

84 

85 

67.88 

51.15 

67.66 

51.45 

67.43 

51.74 

67.21 

52.04 

85 

86 

68.68 

51.76 

68.46 

52.06 

68.23 

52.35 

68.00 

52.65 

86 

87 

69.48 

52.36 

69.25 

52.66 

69.02 

52.96 

68.79 

53.26 

87 

88 

70.28 

52.96 

70.05 

53.27 

69.82 

53.57 

69.58 

53.88 

88 

89 

71.08 

53.56 t 

70.84 

53.87 

70.61 

54.18 

70.37 

54.49 

89 

90 

71.88 

54.16 

71.64 

54.48 

71.40 

54.79 

71.16 

55.10 

90 

91 

72.68 

54.77 

72.44 

55.08 

72.20 

55.40 

71.95 

55.71 

91 

92 

73.47 

55.37 

73.23 

55.69 

72.99 

56.01 

72.74 

56.32 

92 

93 

74.27 

55.97 

74.03 

56.29 

73.78 

56.61 

73.53 

56.94 

93 

94 

75.07 

56.57 

74.82 

56.90 

74.58 

57.22 

74.32 

57.55 

94 ( 

95 

75.87 

57.17 

75.62 

57.50 

75.37 

57.83 

75.12 

58.16 

95 

96 

76.67 

57.77 

76.42 

68.11 

76.16 

58.44 

75.91 

58.77 

96 

97 

77.47 

58.38 

77.21 

58.71 

76.96 

59.05 

76.70 

59.39 

97 

98 

78.27 

58.98 | 

78.01 

59.32 

77.75 

59.66 

77.49 

60.00 

98 

99 

79.06 

59.58 | 

78.80 

59.92 

78.54 

60.27 

78.28 

60.61 

99 

100 

79.86 

60.18 i 

79.60 

60.53 

79.34 

60.88 

79.07 

61.22 

100 

cJ 

o 

Dep. 

Lat. 

Dep. 1 

Lat. 

Dep. 1 

Lat. 

Dep. 1 

Lat. 

• 

o 

o 

c 

m 

c 

53 Deg. 

52| Deg. 

52£ Deg. 

1 

I 

52i Deg. 

a 

-4— 1 

CfJ 

• 

Q 
























































































78 


TRAVERSE TABLE 


0 
*— • 

(J3 

r+- 

P 

38 Deg. 

1 

38i Deg. 

_ 

i 

38£ Deg. 

38| Deg. 

e 

H • 

If) 

r-+ 

P 

P 

s 

o 

» 

Lat. 

Dep. 

Lat. 

Dep. j 

Lat. 

Dep. 

Lat. 

Dep. 

o 

(b 

• j 

1 

0.79 

0.62 

0.79 

0.62 j 

0.78 

0.62 | 

0.78 

0.63 

1 

2 

1.58 

1.23 

1.57 

1.24 

1.57 

1.24 1 

1.56 

1.25 

2 

3 

2.36 

1.85 

2.36 

1.86 

2.35 

1.87 

2.34 

1.88 

3 

4 

3.15 

2.46 

3.14 

2.48 

3.13 

2.49 

3.12 

2.50 

4 

5 

3.94 

3.08 

3.93 

3.10 

3.91 

3.11 

3.90 

3.13 

5 

6 

4.73 

3.69 

4.71 

3.71 

4.70 

3.74 

4.68 

3.76 

6 

7 

5.52 

4.31 

5.50 

4.33 

5.48 

4.36 

5.46 

4.38 

7 

8 

6.30 

4.93 

6.28 

4.95 

6.26 

4.98 

6.24 

5.01 

8 

9 

7.09 

5.54 

7.07 

5.57 

7.04 

5.60 

7.02 

5.63 

9 

10 

7.88 

6.16 

7.85 

6.19 

7.83 

6.23 

7.80 

6.26 

10 

11 

8.67 

6.77 

8.64 

6.81 

8.61 

6.85 

8.58 

6.89 

11 

12 

9.46 

7.39 

9.42 

7.43 

9.39 

7.47 

9.36 

7.51 

12 

13 

10.24 

8.00 

10.21 

8.05 

10.17 

8.09 

10.14 

8.14 

13 

14 

11.03 

8.62 

I 10.99 

8.67 

10.96 

8.72 

10.92 

8.76 

14 

15 

11.82 

9.23 

11.78 

9.29 

11.74 

9.34 

11.70 

9.39 

15 

16 

12.61 

9.85 

12.57 

9.91 

12.52 

9.96 

12.48 

10.01 

16 

17 

13.40 

10.47 

13.35 

10.52 

13.30 

10.58 

13.26 

10.64 

17 

18 

14.18 

11.08 

j 14.14 

11.14 

14.09 

11.21 

14.04 

11.27 

18 

19 

14.97 

11.70 

14.92 

11.76 

14.87 

11.83 

14.82 

11.89 

19 

20 

15.76 

12.31 

15.71 

12.38 

15.65 

12.45 

15.60 

12.52 

20 1 

21 

16.55 

12.93 

j 16.49 

13.00 

16.43 

13.07 

16.38 

13.14 

21 

22 

17.34 

13.54 

| 17.28 

13.62 

17.22 

13.70 

17.16 

13.77 

22 

23 

18.12 

14.16 

18.06 

14.24 

18.00 

14.32 

17.94 

14.40 

23 

24 

18.91 

14.78 

! 18.85 

14.86 

18.78 

14.94 

18.72 

15.02 

24 

25 

19.70 

15.39 

19.63 

15.48 

19.57 

15.56 

19.50 

15.65 

25 

26 

20.49 

16.01 

20.42 

16.10 

20.35 

16.19 

20.28 

16.27 

26 

27 

21.28 

16.62 

21.20 

16.72 

21.13 

16.81 

21.06 

16.90 

27 

28 

22.06 

17.24 

21.99 

17.33 

21.91 

17.43 

21.84 

17.53 

28 

29 

22.85 

17.85 

22.77 

17.95 

22.70 

18.05 

22.62 

18.15 

29 

30 

23.64 

18.47 

23.56 

18.57 

23.48 

18.68 

23.40 

18.78 

30 

31 

24.43 

19.09 

24.34 

19.19 

24.26 

19.30 

24.18 

19.40 

1 

31 

32 

25.22 

19.70 

25.13 

19.81 

25.04 

19.92 

24.96 

20.03 

32 

33 

26.00 

20.32 

25.92 

20.43 

25.83 

20.54 

25.74 

20.66 

33 

34 

26.79 

20.93 

26.70 

21.05 

26.61 

21.17 

26.52 

21.28 

34 

35 

27.58 

21.55 

27.49 

21.67 

27.39 

21.79 

27.30 

21.91 

35 

36 

28.37 

22.16 

28.27 

22.29 

28.17 

22.41 

28.08 

22.53 

36 

37 

29.16 

22.78 

29.06 

22.91 

28.96 

23.03 

28.86 

23.16 

37 

38 

29.94 

23.40 

29.84 

23.53 

1 29.74 

23.66 

29.64 

23.79 

38 

39 

30.73 

24.01 

30.63 

24.14 

30.52 

24.28 

30.42 

24.41 

39 

40 

31.52 

24.63 

31.41 

24.76 

31.30 

24.90 

31.20 

25.04 

40 

41 

32.31 

25.24 

32.20 

25.38 

| 32.09 

25.52 

31.98 

25.66 

41 

42 

33.10 

25.86 

32.98 

26.00 

32.87 

26.15 

32.76 

26.29 

42 

43 

33.88 

26.47 

33.77 

26.62 

33.65 

26.77 

33.53 

26.91 

43 

44 

34.67 

27.09 

34.55 

27.24 

34.43 

27.39 

34.31 

27.54 

44 

45 

35.46 

27.70 

35.34 

27.86 

35.22 

28.01 

35.09 

28.17 

45 

46 

36.25 

28.32 

36.12 

28.48 

36.00 

28.64 

35.87 

28.79 

46 

47 

37.04 

28.94 

36.91 

29.10 

36.78 

29.26 

36 65 

29.42 

47 

48 

37.82 

29.55 

37.70 

29.72 

37.57 

29.88 

37.43 

30.04 

48 

49 

38.61 

30.17 

38.48 

30.34 

38.35 

30.50 

38.21 

30.67 

49 | 

50 

39.40 

30.78 

39.27 

30.95 

39.13 

31.13 

38.99 

31.30 

50 1 

«j 

o 

c 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

<u 

2 I 

cc 

Q 

52 Deg. 

613 Deg. 

51 i Deg. 

51^ Deg. 

d « 

■M | 

/. 

• 

Q 
































































































TRAVERSE TABLE 


79 


Distance, j 

38 Deg. 

38i Deg. 

38^ Deg. 

S8f Deg. 

Distance. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

51 

40.19 

31.40 

40.05 

31.57 

39.91 

31.75 

39.77 

31.92 

51 

52 

40.98 

32.01 

40.84 

32.19 

40.70 

32.37 

40.55 

32.55 

52 

53 

41.76 

32.63 

41.62 

32.81 

41.48 

32.99 

41.33 

33.17 

53 

54 

42.55 

33.25 

42.41 

33.43 

42.26 

33.62 

42.11 

33.80 

54 

55 

43.34 

33.86 

43.19 

34.05 

43.04 

34.24 

42.89 

34.43 

55 

56 

44,13 

34.48 

43.98 

34.67 

43.83 

34.86 

43.67 

35.05 

56 

57 

44.92 

35.09 

44.76 

35.29 

44.61 

35.48 

44.45 

35.68 

57 

58 

45.70 

35.71 

45.55 

35.91 

<45.39 

36.11 

45.23 

36.30 

58 

59 

46.49 

36.32 

46.33 

36.53 

46.17 

36.73 

46.01 

36,93 

59 

60 

47.28 

36.94 

47.12 

37.15 

46.96 

37.35 

46.79 

37.56 

60 

61 

48.07 

37.56 

47.90 

37.76 

47.74 

37.97 

47.57 

38.18 

61 

62 

48.86 

38.17 

48.69 

38.38 

48.52 

38.60 

48.35 

38.81 

62 

63 

49.64 

38.79 

49.47 

39.00 

49.30 

39.22 

49.13 

39.43 

63 

64 

50.43 

39.40 

50.26 

39.62 

50.09 

39.84 

49.91 

40.06 

64 

65 

51.22 

40.02 

51.05 

40.24 

50.87 

40.46 

50.69 

40.68 

65 

66 

52.01 

40.63 

51.83 

40.86 

51.65 

41.09 

51.47 

41.31 

66 

67 

52.80 

41.25 

52.62 

41.48 

52.43 

41.71 

52.25 

41.94 

67 

68 

53.58 

41.86 

53.40 

42.10 

53.22 

42.33 

53.03 

42.56 

68 

69 

54.37 

42,48 

54.19 

42.72 

54.00 

42.95 

53.81 

43.19 

69 

70 

55.16 

43.10 

54.97 

43.34 

54.78 

43.58 

54.59 

43.81 

70 

71 

55.95 

43.71 

55.76 

43.96 

55.57 

44.20 

55.37 

44.44 

71 

72 

56.74 

44.33 

56.54 

44.57 

56.35 

44.82 

56.15 

45.07 

72 

73 

57.52 

44.94 

57.33 

45.19 

57.13 

45.44 

56.93 

45.69 

73 

74 

58.31 

45.56 

58.11 

45.81 

57.91 

46.07 

57.71 

46.32 

74 

75 

59.10 

46.17 

58.90 

46.43 

58.70 

46.69 

58.49 

46.94 

75 

76 

59.89 

46.79 

59.68 

47.05 

59.48 

47.31 

59.27 

47.57 

76 

77 

60.68 

47.41 

60.47 

47.67 

60.26 

47.93 

60.05 

48.20 

77 

78 

61.46 

48.02 

61,25 

48.29 

61.04 

48.56 

60.83 

48.82 

78 

79 

62.25 

48.64 

62.04 

48.91 

61.83 

49.18 

| 61.61 

49.45 

79 

80 

63.04 

49.25 

62.83 

49.53 

j 62.61 

l 

49.80 

62.39 

50.07 

80 

81 

63.83 

49.87 

63.61 

50.15 

63.39 

50.42 

| 63.17 

50.70 

81 

82 

64.62 

50.48 

64.40 

50.77 

64.17 

51.05 

63.95 

51.33 

82 

83 

65.40 

51.10 

65.18 

51.38 

64.96 

51.67 

64.73 

51.95 

83 

84 

66.19 

51.72 

65.97 

52.00 

65.74 

52.29 

65.51 

52.58 

84 

85 

66.98 

52.33 

66.75 

52.62 

66.52 

52.91 

66.29 

53.20 

85 

86 

67.77 

52.95 

67.54 

53.24 

67.30 

53.54 

67.07 

53.83 

86 

87 

68.56 

53.56 

68.32 

53.86 

68.09 

54.16 

67.85 

54.46 

87 

88 

69.34 

54.18 

69.11 

54.48 

68.87 

54.78 

68.63 

55.08 

88 

89 

70.13 

54.79 

69.89 

55.10 

69.65 

55.40 

69.41 

55.71 

89 

90 

70,92 

55.41 

70.68 

55.72 

70.43 

56.03 

70.19 

56.33 

90 

91 

71.71 

56.03 

71.46 

56.34 

71.22 

56.65 

70.97 

56.96 

91 

92 

72,50 

56.64 

72.25 

56.96 

72.00 

57.27 

71.75 

57.58 

92 

93 

73.28 

57.26 

73.03 

57.58 

72.78 

57.89 

72.53 

58.21 

93 

94 

74.07 

57.87 

73.82 

58.19 

73.57 

58.52 

73.31 

58.84 

94 

95 

74.86 

58.49 

74.61 

58.81 

74.35 

59.14 

74.09 

59,46 

95 

96 

75.65 

59.10 

75.39 

59,43 

75.13 

59.76 

74.87 

60.09 

96 

97 

76.44 

59.72 

76.18 

60.05 

75.91 

60.38 

75.65 

60.71 

97 

98 

77.22 

60.33 

76.96 

60.67 

76.70 

61.01 

76.43 

61.34 

98 

99 

78.01 

60.95 

77,75 

61.29 

77.48 

61.63 

77.21 

61.97 

99 

100 

78.80 

61.57 

78.53 

61.91 

78.26 

62.25 

77.99 

62.59 

100 

y 

o 

Dep. 

Lat. 

Dep. 

Lat, 

Dep. 

Lat. 

Dep. 

Lat. 

® 

y 

G 

C#3 

5 

62 Deg. 

611 Deg. 

61 £ Deg. 

6U Deg. 

+-» 

c n 

Q 





















































































80 


TRAVERSE TABLE 


a 

in 

rt* 

V 

39 Deg. 

39i 

Deg. 

39£ 

Deg. 

1 

39f 

Deg. 

D 
►—. 
rn 
r-f 

P 

cs 

o 

(D 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

o 

K> 

1 

0.78 

0.63 

0.77 

0.63 

0.77 

0.64 

0.77 

0.64 

1 

2 

1.55 

1.26 

1.55 

1.27 

1.54 

1.27 

1.54 

1.28 

2 

3 

2.33 

1.89 

2.32 

1.90 

2.31 

1.91 

2.31 

1.92 

3 

4 

3.11 

2.52 

3.10 

2.53 

3.09 

2.54 

3.08 

2.56 

4 

5 

3.89 

3.15 

3.87 

3.16 

3.86 

3.18 

3.84 

3.20 

5 

6 

4.66 

3.78 

4.65 

3.80 

4.63 

3.82 

4.61 

3.84 

6 

7 

5.44 

4.41 

5.42 

4.43 

5.40 

4.45 

5.38 

4.48 

7 

8 

6.22 

5.03 

6.20 

5.06 

6.17 

5.09 

6.15 

5.12 

8 

9 

6.99 

5.66 

6.97 

5.69 

6.94 

5.72 

6.92 

5.75 

9 

10 

7.77 

6.29 

7.74 

6.33 

7.72 

6.36 

7.69 

6.39 

10 

11 

8.55 

6.92 

8.52 

6.96 

8.49 

7.00 

8.46 

7.03 

11 

12 

9.33 

7.55 

9.29 

7.59 

9.26 

7.63 

9.23 

7.67 

12 

13 

10.10 

8.18 

10.07 

8.23 

10.03 

8.27 

9.99 

8.31 

13 

14 

10.88 

8.81 

10.84 

8.86 

10.80 

8.91 

10.76 

8.95 

14 

15 

11.66 

9.44 

11.62 

9.49 

11.57 

9.54 

11.53 

9.59 

15 

16 

12.43 

10.07 

12.39 

10.12 

12.35 

10.18 

12.30 

10.23 

16 

17 

13.21 

10.70 

13.16 

10.76 

13.12 

10.81 

13.07 

10.87 

17 

18 

13.99 

11.33 

13.94 

11.39 

13.89 

11.45 

13.84 

11.51 

18 

19 

14.77 

11.96 

14.71 

12.02 

14.66 

12.09 

14.61 

12.15 

19 

20 

15.54 

12.59 

15.49 

12.65 

15.43 

12.72 

15.38 

12.79 

20 

21 

16.32 

13.22 

16.26 

13.29 

16.20 

13.36 

16.15 

13.43 

21 

22 

17.10 

13.84 

17.04 

13.92 

16.98 

13.99 

16.91 

14.07 

22 

23 

17.87 

14.47 

17.81 

14.55 

17.75 

14.63 

17.68 

14.71 

23 

24 

18.65 

15.10 

18.59 

15.18 

18.52 

15.27 

18.45 

15.35 

24 

25 

19.43 

15.73 

19.36 

15.82 

19.29 

15.90 

19.22 

15.99 

25 

26 

20.21 

16.36 

20.13 

16.45 

20.06 

16.54 

19.99 

16.63 

26 

27 

20.98 

16.99 

20.91 

17.08 

20.83 

17.17 

20.76 

17.26 

27 

28 

21.76 

17.62 

21.68 

17.72 

21.61 

17.81 

21.53 

17.90 

28 

29 

22.54 

18.25 

22.46 

18.35 

22.38 

18.45 

22.30 

18.54 

29 

30 

23.31 

18.88 

23.23 

18.98 

23.15 

19.08 

23.07 

19.18 

30 

31 

24.09 

19.51 

24.01 

19.61 

23.92 

19.72 

23.83 

19.82 

31 

32 

24.87 

20.14 

24.78 

20.25 

24.69 

20.35 

24.60 

20.46 

32 

33 

25.65 

20.77 

25.55 

20.88 

25.46 

20.99 

25.37 

21.10 

33 

34 

26.42 

21.40 

26.33 

21.51 

26.24 

21.63 

26.14 

21.74 

34 

35 

27.20 

22.03 

27.10 

22.14 

27.01 

22.26 

26.91 

22.38 

35 

36 

27.98 

22.66 

27.88 

22.78 

27.78 

22.90 

27.68 

23.02 

36 

37 

28.75 

23*28 

28.65 

23.41 

28.55 

23.53 

28.45 

23.66 

37 

38 

29.53 

23.91 

29.43 

24.04 

29.32 

24.17 

29.22 

24.30 

38 

39 

30.31 

24.54 

30.20 

24.68 

30.09 

24.81 

29.98 

24.94 

39 

40 

31.09 

25.17 

30.98 

25.31 

30.86 

25.44 

30.75 

25.58 

40 

41 

31.86 

25.80 

31.75 

25.94 

31.64 

26.08 

31.52 

26.22 

41 

42 

32.64 

26.43 

32.52 

26.57 

32.41 

26.72 

32.29 

26.86 

42 

43 

33.42 

27.06 

33.30 

27.21 

33.18 

27.35 

33.06 

27.50 

43 

44 

34.19 

27.69 

34.07 

27.84 

33.95 

27.99 

33.83 

28.14 

44 

45 

34.97 

28.32 

34.85 

28.47 

34.72 

28.62 

34.60 

28.77 

45 

46 

35.75 

28.95 

35.62 

29.10 

35.49 

29.26 

35.37 

29.41 

46 

47 

36.53 

29.58 

36.40 

29.74 

36.27 

29.90 

36.14 

30.05 

47 

48 

37.30 

30.21 

37.17 

30.37 

37.04 

30.53 

36.90 

30.69 

48 

49 

38.08 

30.84 

37.95 

31.00 

37.81 

31.17 

37.67 

31.33 

49 

50 

38.86 

31.47 

38.72 

31.64 

38.58 

31.80 

38.44 

31.97 

50 

4 ) 

O 

jj 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

o 

«5 

*4-> 

<n 

Q 

51 Deg. 

50$ 

Deg. 

50^ Deg. 

50$ Deg. 

CC 

• H 

o 


/ 
















































































TRAVERSE TABLE 


81 


a 

M . 

OD 

P 

39 

Deg. 

39! Deg. 

39! Deg. 

V 

1 

39| Deg. 

0 

. 

r-t* 

p 

o 

ct> 

• 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

| — 
Lat. 

Dep. 

3 

o 

CD 

51 

39.63 

32.10 

39.49 

32.27 

39.35 

32.44 

39.21 

32.61 

51 

52 

40.41 

32.72 

40.27 

32.90 

40.12 

33.08 

39.98 

33.25 

52 

53 

41.19 

33.35 

41.04 

33.53 

40.90 

33.71 

40.75 

33.89 

53 

54 

41.97 

33.98 

41.82 

34.17 

41.67 

34.35 

41.52 

34.53 

54 

55 

42.74 

34.61 

42.59 

34.80 

42.44 

34.98 

42.29 

35.17 

55 

56 

43.52 

35.24 

43.37 

35.43 

43.21 

35.62 

43.06 

35.81 

56 

57 

44.30 

35.87 

44.14 

36.06 

43.98 

36.26 

43.82 

36.45 

57 

58 

45.07 

36.50 

44.91 

36.70 

44.75 

36.89 

44.59 

37.09 

58 

59 

45.85 

37.13 

45.69 

37.33 

45.53 

37.53 

45.36 

37.73 

59 

60 

46.63 

37.76 

46.46 

37.96 

46.30 

38.16 

46.13 

38.37 

60 

61 

47.41 

38.39 

47.24 

38.60 

47.07 

38.80 

46.90 

39.01 

61 

62 

48.18 

39.02 

48.01 

39.23 

47.84 

39.44 

47.67 

39.65 

62 

63 

48.96 

39.65 

48.79 

39.86 

48.61 

40.07 

48.44 

40.28 

63 

64 

49.74 

40.28 

49.56 

40.49 

49.38 

40.71 

49.21 

40.92 

64 

65 

50.51 

40.91 

50.34 

41.13 

50.16 

41.35 

49.97 

41.56 

65 

66 

51.29 

41.54 

51.11 

41.76 

50.93 

41.98 

50.74 

42.20 

66 

67 

52.07 

42.16 

51.88 

42.39 

51.70 

42.62 

51.51 

42.84 

67 

68 

52.85 

42.79 

52.66 

43.02 

52.47 

43.25 

52.28 

43.48 

68 

69 

53.52 

43.42 

53.43 

43.66 

53.24 

43.89 

53.05 

44.12 

69 

70 

54.40 

44.05 

54.21 

44.29 

54.01 

44.53 

53.82 

44.76 

70 

71 

55.18 

44.68 

54.98 

44.92 

54.79 

45.16 

54.59 

45.40 

71 

72 

55.95 

45.31 

55.76 

45.55 

55.56 

45.80 

55.36 

46.04 

72 

73 

56.73 

45.94 

56.53 

46.19 

56.33 

46.43 

56.13 

46.68 

73 

74 

57.51 

46.57 

57.31 

46.82 

57.10 

47.07 

56.89 

47.32 

74 

75 

58.29 

47.20 

58.08 

47.45 

57.87 

47.71 

57.66 

47.96 

75 

76 

59.06 

47.83 

58.85 

48.09 

58.64 

48.34 

58.43 

48.60 

76 

77 

59.84 

48.46 

59.63 

48.72 

59.42 

48.98 

59.20 

49.24 

77 

78 

60.62 

49.09 

60.40 

49.35 

60.19 

49.61 

59.97 

49.88 

78 

79 

61.39 

49.72 

61.18 

49.98 

60.96 

50.25 

60.74 

50.52 

79 

80 

62.17 

50.35 

61.95 

50.62 

61.73 

50.89 

61.51 

51.16 

80 

81 

62.95 

50.97 

62.73 

51.25 

62.50 

51.52 

62.28 

51.79 

81 

82 

63.73 

51.60 

63.50 

51.88 

63.27 

52.16 

63.04 

52.43 

82 

83 

64.50 

52.23 

64.27 

52.51 

64.04 

52.79 

63.81 

53.07 

83 

84 

65.28 

52.86 

65.05 

53.15 

64.82 

53.43 

64.58 

53.71 

84 

85 

66.06 

53.49 

65.82 

53.78 

65.59 

54.07 

65.35 

54.35 

85 

86 

66.83 

54.12 

66.60 

54.41 

66.36 

54.70 

66.12 

54.99 

86 

87 

67.61 

54.75 

67.37 

55.05 

67.13 

55.34 

66.89 

55.63 

87 

88 

68.39 

55.38 

68.15 

55.68 

67.90 

55.97 

67.66 

56.27 

88 

89 

69.17 

56.01 

68.92 

56.32 

68.67 

56.61 

68.43 

56.91 

89 

90 

69.94 

56.64 

69.70 

56.94 

69.45 

57.25 

69.20 

57.55 

90 

91 

70.72 

57.27 

70.47 

57.58 

70.22 

57.88 

69.96 

58.19 

91 

92 

71.50 

57.90 

71.24 

58.21 

70.99 

58.52 

70.73 

58.83 

92 

93 

72.27 

58.53 

72.02 

58.84 

71.76 

59.16 

71.50 

59.47 

93 

94 

73.05 

59.16 

72.79 

59.47 

72.53 

59.79 

72.27 

60.11 

94 

95 

73.83 

59.79 

73.57 

60.11 

73.30 

60.43 

73.04 

60.75 

95 

96 

74.61 

60.41 

74.34 

60.74 

74.08 

61.06 

73.81 

61.39 

96 

97 

75.38 

61.04 

75.12 

61.37 

74.85 

61.70 

74.58 

62.03 

97 

98 

76.16 

61.67 

75.89 

62.01 

75.62 

62.34 

75.35 

62.66 

98 | 

99 

76.94 

62.30 

76.66 

62.64 

76.39 

62.97 

76.12 

63.30 

99 

100 

77.71 

62.93 

77.44 

63.27 

77.16 

63.61 | 

76.88 

63.94 

100 f 

6 

o 

Dep. 

Lat. 

Dep. 

Lat. | 

Dep. 

Lat. j 

Dep. | 

Lat. 

6 | 
o 2 

.3 I 

' -4-> 

m 

• 

a 

51 Deg. 

--- . ■■ . Vr-s- 

50f Deg. 

1 

50! Deg. 

50! Deg. 

cG J 

• - i 

rfl H 

s 

1 


L 


























































































































82 


TRAVERSE TABLE 


Distance. 

! 

40 Deg. 

I 

40-} Deg. 

40} Deg. 

i 

40} Deg. 

0 

t/J * 

g 

S 

a 

a 

Lat. 

Dep. 

Lat. 

i 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

1 

0.77 

0.64 

0.76 

0.65 

0.76 

0.65 

0.76 

0.65 

1 

2 

1.53 

1.29 

1.53 

1.29 

1.52 

1.30 

1.52 

1.31 

2 

3 

2.30 

1.93 

2.29 

1.94 

2.28 

1.95 

2.27 

1.96 

3 

4 

3.06 

2.57 

3.05 

2.58 

3.04 

2.60 | 

3.03 

2.61 

4 

5 

3.83 

3.21 

3.82 

3.23 

3.80 

3.25 

3.79 

3.26 

5 

6 

4.60 

3.86 

4.58 

3.88 

4.56 

3.90 

4.55 

3.92 

6 

7 

5.36 

4.50 

5.34 

4.52 

5.32 

4.55 

5.30 

4*. 57 

7 

8 

6.13 

5.14 

6.11 

5.17 

6.08 

5.20 

6.06 

5.22 

8 

9 

6.89 

5.79 

6.87 

5.82 

6.84 

5.84 

6.82 

5.87 

9 

10 

7.66 

6.43 

7.63 

6.46 

7.60 

6.49 

7.58 

6.53 

10 

11 

8.43 

7.07 

8.40 

7.11 | 

8.36 

%• 14 

8.33 

7.18 

11 

12 

9.19 

7.71 

9.16 

7.75 

9.J2 

7.79 

9.09 

7.83 

12 

13 

9.96 

8.36 

9.92 

8.40 

9 .‘89 

8.44 

9.85 

8.49 

13 

14 

10.72 

9.00 

10.69 

9.05 

10.65 

9.09 

10.61 

9.14 

14 

15 

11.49 

9.64 

11.45 

9.69 

11.41 

9.74 

11.36 

9.79 

15 

16 

12.26 

10.28 

12.21 

10.34 

12.17 

10.39 

12.12 

10.44 

16 

17 

13.02 

10.93 

12.97 

10.98 

12.93 

11.04 

12.88 

11.10 

17 

[■ 18 

13.79 

11.57 

13.74 

11.63 

13.69 

11.69 

13.64 

11.75 

18 

19 

14.55 

12.21 

14.50 

12.28 

14.45 

12.34 

14.39 

12.40 

19 

20 

15.32 

12.86 

15.26 

12.92 

15.21 

12.99 

15.15 

13.06 

20 

21 

16.09 

13.50 

16.03 

13.57 

15.97 

13.64 II 15.91 

13.71 

21 

22 

16.85 

14.14 

16.79 

14.21 

16.73 

14.29 

16.67 

14.36 

22 

23 

17.62 

14.78 

17.55 

14.86 

17.49 

14.94 

17.42 

15.01 

23 

24 

18-39 

15.43 

18.32 

15-51 

18.25 

15.59 

18.18 

15.67 

24 

! 25 

19.15 

16.07 

19.08 

16.15 

19.01 

16.24 

18.94 

16.32 

25 

; 26 

19.92 

16.71 

19.84 

16.80 

19.77 

16.89 

19.70 

16.97 

26 

27 

20.68 

17.36 

20.61 

17.45 

20.53 

17.54 

20.45 

17.62 

27 

28 

21.45 

18.00 

21.37 

18.09 

21.29 

18.18 

21.21 

18.28 

28 1 

29 

22.22 

18.64 

22.13 

18.74 

22.05 

18.83 

21.97 

18.93 

29 

30 

22.98 

19.28 

22.90 

19.38 

22.81 

19.48 

22.73 

19.58 

30 

31 

23.75 

19.93 

23.66 

20.03 

23.57 

20.13 

23.48 

20.24 

31 

32 

24.51 

20.57 

24.42 

20.68 

24.33 

20.73 

24.24 

20.89 

32 

33 

25.28 

21.21 

25.19 

21.32 

25.09 

21.43 

25.00 

21.54 

33 

1 34 

26.05 

21.85 

25.95 

21.97 

25.85 

22.08 

25.76 

22.19 

34 

: 35 

26.81 

22.50 

26.71 

22.61 

26.61 

22.73 

26.51 

22.85 

35 

1 36 

27.58 

23.14 

27.48 

23.26 

27.37 

23.38 

27.27 

23.50 

36 

37 

28.34 

23.78 

28.24 

23.91 

28.13 

24.03 

28.03 

24.15 

37 

| 38 

29.11 

24.43 

29.00 

24.55 

28.90 

24.68 

28.79 

24.80 

38 

39 

29.88 

25.07 

29.77 

25.20 

29.66 

25.33 

29.54 

25.46 

39 

I 40 

30.64 

25.71 

30.53 

25.84 

30.42 

25.98 

30.30 

26.11 

40 

' 41 

31.41 

26.35 

31.29 

26.49 

31.18 

26.63 

31.06 

26.76 

41 

; 42 

32.17 

27.00 

32.06 

27.14 

31.94 

27.28 

31.82 

27.42 

42 

j 43 

32.94 

27.64 

32.82 

27.73 

32.70 

27.93 

32.53 

28.07 

43 

. 44 

33.71 

28.28 

33.58 

28.43 

33.46 

28.58 

33.33 

28.72 

44 

J 45 

34.47 

28.93 

34.35 

29.08 

34.22 

29.23 

34.09 

29.37 

45 

46 

35.24 

29.57 

35.11 

29.72 

34.98 

29.87 

34.85 

30.03 

46 

47 

36.00 

30.21 

35.87 

30.37 

35.74 

30.52 

35.61 

30.68 

47 

I 48 

36.77 

30.85 

36.64 

31.01 

36.50 

31.17 

36.36 

31.33 

48 

; 49 

37.54 

31.50 

37.40 

31.66 

37.26 

31.82 

37.12 

31.99 

49 

I 50 

38.30 

32.14 

38.16 

32.31 

38.02 

32.47 

37.88 

32.64 

50 

| Distance. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Distance. 

50 Deg. 

49} Deg. 

49} Deg. 

| 

1 

49} Deg. 



































































































TRAVERSE TABLE 


83 


Distance. 

40 Deg. 

40i Deg. 

40J Deg. 

40f Deg. 

| Distance. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

51 

39.07 

32.78 

38.92 

32.95 

38.78 

33.12 

38.64 

33.29 

51 

52 

39.83 

33.42 

39.69 

33.60 

39.54 

33.77 

39.39 

33.94 

52 

53 

40.60 

34.07 

40.45 

34.24 

40.30 

34.42 

40.15 

34.60 

53 

54 

41.37 

34.71 

41.21 

34.89 

41.06 

35.07 

40.91 

35.25 

54 

55 

42.13 

35.35 

41.98 

35.54 

41.82 

35.72 

41.67 

35.90 

55 

56 

42.90 

36.00 

42.74 

36.18 

42.58 

36.37 

42.42 

36.55 

56 

57 

43.66 

36.64 

43.50 

36.83 

43.34 

37.02 

43.18 

37.21 

57 

58 

44.43 

37.28 

44.27 

37.48 

44.10 

37.67 

43.94 

37.86 

58 

59 

45.20 

37.92 

45.03 

38.12 

44.86 

38.32 

44.70 

38.51 

59 

60 

45.96 

38.57 

45.79 

38.77 

45.62 

38.97 

45.45 

39.17 

60 

61 

46.73 

39.21 

46.56 

39.41 

46.38 

39.62 

46.21 

39.82 

61 

62 

47.49 

39.85 

47.32 

40.06 

47.15 

40.27 

46.97 

40.47 

62 

63 

48.26 

40.50 

48.08 

40.71 

47.91 

40.92 

47.73 

41.12 

63 

64 

49.03 

41.14 

48.85 

41.35 

48.67 

41.56 

48.48 

41.78 

64 

65 

49.79 

41.78 

49.61 

42.00 

49.43 

42.21 

49.24 

42.43 

65 

66 

50.56 

42.42 

50.37 

42.64 

50.19 

42.86 

50.00 

43.08 

66 

67 

51.32 

43.07 

51.14 

43.29 

50.95 

43.51 

50.76 

43.73 

67 

68 

52.09 

43.71 

51.90 

43.94 

51.71 

44.16 

51.51 

44.39 

68 

69 

52.86 

44.35 

52.66 

44.58 

52.47 

44.81 

52.27 

45.04 

69 

70 

53.62 

45.00 

53.43 

45.23 

53.23 

45.46 

53.03 

45.69 

70 

71 

54.39 

45.64 

54.19 

45.87 

53.99 

46.11 

53.79 

46.35 

71 

72 

55.16 

46.28 

54.95 

46.52 

54.75 

46.76 

54.54 

47.00 

72 

73 

55.92 

46.92 

55.72 

47.17 

55.51 

47.41 

55.30 

47.65 

73 

74 

56.69 

47.57 

56.48 

47.81 

56.27 

48.06 

56.06 

48.30 

74 

75 

57.45 

48.21 

57.24 

48.46 

57.03 

48.71 

56.82 

48.96 

75 

76 

58.22 

48.85 

58.01 

49.11 

57.79 

49.36 

57.57 

49.61 

76 

77 

58.99 

49.49 

58.77 

49.75 

58.55 

50.01 

58.33 

50.26 

77 

78 

59.75 

50.14 

59.53 

50.40 

59.31 

50.66 

59.09 

50.92 

78 

79 

60.52 

50.78 

60.30 

51.04 

60.07 

51.31 

59.85 

51.57 

79 

80 

61.28 

51.42 

61.06 

51.69 

60.83 

51.96 

60.61 

52.22 

80 

81 

62.05 

52.07 

61.82 

52.34 

61.59 

52.61 

61.36 

52.87 

81 

82 

62.82 

52.71 

62.59 

52.98 

62.35 

53.25 

62.12 

53.53 

82 

83 

63.58 

53.35 

63.35 

53.63 

63.11 

53.90 

62.88 

54.18 

83 

84 

64.35 

53.99 

64.11 

54.27 

63.87 

54.55 

63.64 

54.83 

84 

85 

65.11 

54.64 

64.87 

54.92 

64.63 

55.20 

64.39 

55.48 

85 

86 

65.88 

55.28 

65.64 

55.5 7 

65.39 

55.85 

65.15 

56.14 

86 

87 

66.65 

55.92 

66.40 

56.21 

66.16 

56.50 

65.91 

56.79 

87 

88 

67.41 

56.57 

67.16 

56.86 

66.92 

57.15 

66.67 

57.44 

88 

89 

68.18 

57.21 

67.93 

57.50 

67.68 

57.80 

67.42 

58.10 

89 

90 

68.94 

57.85 

68.69 

58.15 

68.44 

58.45 

68.18 

58.75 

90 

91 

69.71 

58.49 

69.45 

58.80 

69.20 

59.10 

68.94 

59.40 

91 \ 

92 

70.48 

59.14 

70.22 

59.44 

69.96 

59.75 

69.70 

60.05 

92 

93 

71.24 

59.78 

70.98 

60.09 

70.72 

60- 40 

70.45 

60.71 

93 

94 

72.01 

60.42 

71.74 

60.74 

71.48 

61.05 

71.21 

61.36 

94 

95 

72.77 

61.06 

72.51 

61.38 

72.24 

61.70 

71.97 

62.01 

95 

96 

73.54 

61.71 

73.27 

62.03 

73.00 

62.35 

72.73 

62.66 

96 

97 

74.31 

62.35 

74.03 

62.67 

73.76 

63.00 

73.48 

63.32 

97 

98 

75.07 

62.99 

74.80 

63.32 

74.52 

63.65 

74.24 

63.97 

98 

99 

75.84 

63.64 

75.56 

63.97 

75.28 

64.30 

75.00 

64.62 

99 

100 

76.60 

64.28 

76.32 

64.61 

76.04 

64.94 

75.76 

65.28 

100 

oi 

o 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

o 

c 

£ 

CTJ 

m 

• '•H 

Q 

50 Deg. 

49| Deg. 

49 i Deg. 

49£ Deg. 

C t 

Of) 

• ^4 

° 




















































































TRAVERSE TABLE 


84 


i 

g 

LT> ’ 

P 

41 Deg. 

4U 

Deg. 

41 $ Deg. 

41| 

Deg. 

© 

H . 

V) 

p 

E3 

o 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

o 

o 

• 

1 

0.75 

0.66 

0.75 

0.66 

0.75 

0.66 

0.75 

0.67 

1 

2 

1.51 

1.31 

1.50 

1.32 

1.50 

1.33 

1.49 

1.13 

2 

3 

2.26 

1.97 

2.26 

1.98 

2.25 

1.99 

2.24 

2.00 

3 

4 

3.02 

2.62 

3.01 

2.64 

3.00 

2.65 

2.98 

2.66 

4 

5 

3.77 

3.28 

3.76 

3.30 

3.74 

3.31 

3.73 

3.33 

5 1 

6 

4.53 

3.94 

4.51 

3.96 

4.49 

3.98 

4.48 

4.00 

6 

7 

5.28 

4.59 

5.26 

4.62 

5.24 

4.64 

5.22 

4.66 

7 

! 8 

6.04 

5.25 

6.01 

5.27 

5.99 

5.30 

5.97 

5.33 

8 

9 

6.79 

5.90 

6.77 

5.93 

6.74 

5.96 

6.71 

5.99 

9 

10 

7.55 

6.56 

7.52 

6.59 

7.49 

6.63 

7.46 

6.66 

10 

11 

8.30 

7.22 

8.27 

7.25 

8.24 

7.29 

8.21 

7.32 

11 

12 

9.06 

7.87 

9.02 

7.91 

8.99 

7.95 

8.95 

7.99 

12 

13 

9.81 

8.53 

9.77 

8.57 

9.74 

8.61 

9.70 

8.66 

13 

! 14 

10.57 

9.18 

10.53 

9.23 

10.49 

9.28 

10.44 

9.32 

14 

15 

11.32 

9.84 

11.28 

9.89 

11.23 

9.94 

11.19 

9.99 

15 

16 

12.08 

10.50 

12.03 

10.55 

11.98 

10.60 

11.94 

10.65 

16 

! 17 

12.83 

11.15 

12.78 

11.21 

12.73 

11.26 

12.68 

11.32 

17 

18 

13.58 

11.81 

13.53 

11.87 

13.48 

11.93 

13.43 

11.99 

18 

19 

14.34 

12.47 

14.28 

12.53 

14.23 

12.59 

14.18 

12.65 

19 [ 

20 

15.09 

13.12 

15.04 

13.19 

14.98 

13.25 

14.92 

13.32 

20 

21 

15.85 

13.78 

15.79 

13.85 

15.73 

13.91 

15.67 

13.98 

21 

22 

16.60 

14.43 

16.54 

14.51 

16.48 

14.58 

16.41 

14.65 

22 

23 

17.36 

15.09 

17.29 

15.16 

17.23 

15.24 

17.16 

15.32 

23 

24 

18.11 

15.75 

18.04 

15.82 

17.97 

15.90 

17.91 

15.98 

24 

25 

■ 18.87 

16.40 

18.80 

16.48 

18.72 

16.57 

18.65 

16.65 

25 

26 

19.62 

17.06 

19.55 

17.14 

19.47 

17.23 

19.40 

17.31 

26 

27 

20.38 

17.71 

20.30 

17.80 

20.22 

17.89 

20.14 

17.98 

27 1 

28 

21.13 

18.37 

21.05 

18.46 

20.97 

18.55 

20.89 

18.64 

28 

29 

21.89 

19.03 

21.80 

19.12 

21.72 

19.22 

21.64 

19.31 

29 

30 

22.64 

19.68 

22.56 

19.78 

22.47 

19.88 

22.38 

19.98 

30 

31 

23.40 

20.34 

23.31 

20.44 

23.22 

20.54 

23.13 

20.64 

31 

32 

24.15 

20.99 

24.06 

21.10 

23.97 

21.20 

23.87 

21.31 

32 

33 

24.91 

21.65 

24.81 

21.76 

24.72 

21.87 

24.62 

21.97 

33 

34 

25.66 

22.31 

25.56 

22.42 

25.46 

22.53 

25.37 

22.64 

34 

35 

26.41 

22.96 

26.31 

23.08 

26.21 

23.19 

26.11 

23.31 

35 

36 

27.17 

23.62 

27.07 

23.74 

26.96 

23.85 

26.86 

23.97 

36 

37 

27.92 

24.27 

27.82 

24.40 

27.71 

24.52 

27.60 

24.64 

37 

38 

28.68 

24.93 

28.57 

25.06 

28.46 

25.18 

28.35 

25.30 

38 

39 

29.43 

25.59 

29.32 

25.71 

29.21 

25.84 

29.10 

25.97 

39 

40 

‘l 

30.19 

26.24 

30.07 

26.37 

29.96 

26.50 

29.84 

26.64 

40 

! 41 

30.94 

26.90 

30.83 

27.03 

30.71 

27.17 

30.59 

27.30 

41 

42 

31.70 

27.55 

31.58 

27.69 

31.46 

27.83 

31.33 

27.97 

42 

43 

32.45 

28.21 

32.33 

28.35 

32.21 

28.49 

32.08 

28.63 

43 

44 

33.21 

28.87 

33.08 

29.01 

32.95 

29.16 

32.83 

29.30 

44 

46 

33.96 

29-52 

33.83 

29.67 

33.70 

29.82 

33.57 

29.97 

45 

46 

34.72 

30.18 

34.58 

30.33 

34.45 

30.48 

34.32 

30.63 

46 

47 

35.47 

30.83 

35.34 

30.99 

35.20 

31.14 

35.06 

31.30 

47 

48 

36.23 

31.49 

36.09 

31.65 

35.95 

31.81 

35.81 

31.96 

48 

49 

36.98 

32.15 

36.84 

32.31 

36.70 

32.47 

36.56 

32.63 

49 

50 

37.74 

32.80 

37.59 

32.97 

37.45 

- 

33.13 

37.30 

33.29 

50 | 

<u 

a 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. | 

Lat. 

Dep. 

Lat. 

6 

o 1 

<?j 

V3 

' “ H 

Q 

— 

49 Deg. 

43f Deg. 

48$ Deg. 

48$ Deg. 

C 

«*-> 

m 

P 






















































































TRAVERSE TABLE 


8f) 


■ »— • 

■ Uj 

1 1 r-t- 

1 V> 

I p 

41 

Deg. 

1 

41i 

Deg. 

41i 

Deg. 

41J 

Deg. 

u 

*—< * 

ID 

r-*~ 

P 

1 o 

I ? 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

a 

o 

m 

• s 

I 51 

38.49 

33.46 

38.34 

33.63 

38.20 

33.79 

38.05 

33.96 

51 

52 

39.24 

34.12 

39.10 

34.29 

38.95 

34.46 

38.79 

34.63 

52 

53 

40.00 

34.77 

39.85 

34.95 

39.69 

35.12 

39.54 

35.29 

53 

54 

40.75 

35.43 

40.60 

35.60 

40.44 

35.78 

40.29 

35.96 

54 

I 55 

41.51 

36.08 

41.35 

36.26 

41.19 

36.44 

41.03 

36.62 

55 

I 56 

42.26 

36.74 

42.10 

36.92 

41.94 

37.11 

41.78 

37.29 

56 

II 57 

43.02 

37.40 

42.85 

37.58 

42.69 

37.77 

42.53 

37.96 

57 

( 58 

43.77 

38.05 

43.61 

38.24 

43.44 

38.43 

43.27 

38.62 

58 

59 

44.53 

38.71 

44.36 

38.90 

44.19 

39.09 

44.02 

39.29 

59 

i 60 

45.28 

39.36 

45.11 

39.56 

44.94 

39.76 

44.76 

39.95 

60 

; 61 

46.04 

<*40.02 

45.86 

40.22 

45.69 

40.42 

45.51 

40.62 

61 

62 

46.79 

40.68 

46.61 

40.88 

46.44 

41.08 

46.26 

41.28 

62 

'' 63 

47.55 

41.33 

47.37 

41.54 

47.18 

41.75 

47.00 

41.95 

63 

1 64 

48.30 

41.99 

48.12 

42.20 

47.93 

42.41 

47.75 

42.62 

64 

I 6 5 

49.06 

42.64 

48.87 

42.86 

48.68 

43.07 

48.49 

43.28 

65 

I 66 

49.81 

43.30 

49.62 

43.52 

49.43 

43.73 

49.24 

43.95 

66 

I 67 

50.57 

43.96 

50.37 

44.18 

50.18 

44.40 

49.99 

44.61 

67 

I 68 

51.32 

44.61 

51.13 

44.84 

50.93 

45.06 

50.73 

45.28 

68 

;■ 69 

52.07 

45.27 

51.88 

45.49 

51.68 

45.72 

51.48 

45.95 

69 

I 70 

52.83 

45.92 

52.63 

46.15 

52.43 

46.38 

52.22 

46.61 

70 

1 71 

53.58 

46.58 

53.38 

46.81 

53.18 

47.05 

52.97 

47.28 

71 

II 72 

54.34 

47.24 

54.13 

47.47 

53.92 

47.71 

53.72 

47.94 

72 

| 73 

55.09 

47.89 

54.88 

48.13 

54.67 

48.37 

54.46 

48.61 

73 

74 

55.85 

48.55 

55.64 

48.79 

55.42 

49.03 

55.21 

49.28 

74 

75 

56.60 

49.20 

56.39 

49.45 

56.17 

49.70 

55.95 

49.94 

75 

L 76 

57.36 

49.86 

57.14 

50.11 

56.92 

50.36 

56.70 

50.61 

76 

j 77 

58.11 

50.52 

57.89 

50.77 

57.67 

51.02 

57.45 

51.27 

77 

78 

58.87 

51.17 

58.64 

51.43 

58.42 

51.68 

58.19 

51.94 

78 

79 

59.62 

51.83 

59.40 

52.09 

59.17 

52.35 

58.94 

52.60 

79 

: 80 

60.38 

52.48 

60.15 

52.75 

59.92 

53.01 

59.68 

53.27 

80 

81 

61.13 

53.14 

60.90 

53.41 

60.67 

53.67 

60.43 

53.94 

81 

1 82 

61.89 

53.80 

61.65 

54.07 

61.41 

54.33 

61.18 

54.60 

82 

S3 

62.64 

54.45 

62.40 

54.73 

62.16 

55.00 

61.92 

55.27 

83 

! 84 

63.40 

55.11 

63.15 

55.38 

62.91 

55.66 

62.67 

55.93 

84 

1 85 

64.15 

55.76 

63.91 

56.04 

63.66 

56.32 

63.41 

56.60 

85 

86 

64.90 

56.42 

64.66 

56.70 

64.41 

56.99 

64.16 

57.27 

86 

1 87 

65.66 

57.08 

65.41 

57.36 

65.16 

57.65 

64.91 

57.93 

87 

1 88 

66.41 

57.73 

66.16 

58.02 

65.91 

58.31 

65.65 

58.60 

88 

f 89 

67.17 

58.39 

66.91 

58.68 

66.66 

58.97 

66.40 

59.26 

89 

90 

67.92 

59.05 

67.67 

59.34 

67.41 

59.64 

67.15 

59.93 

90 

1 91 

68.68 

59.70 

68.42 

60.00 

63.15 

60.30 

67.89 

60.60 

91 

«■ 92 

69.43 

60.36 

69.17 

60.66 

68.90 

60.96 

68.64 

61.26 

92 

l 93 

70.19 

61.01 

69.92 

61.32 

69.65 

61.62 

69.38 

61.93 

93 

I 94 

70.94 

61.67 

70.67 

61.98 

70.40 

62.29 

70.13 

62.59 

94 

95 

71.70 

62.33 

71.43 

62.64 

71.15 

62.95 

70.88 

63.26 

95 

|! 96 

72.45 

62.98 

72.18 

63.30 

71.90 

63.61 

71.62 

63.92 

96 

L 97 

73.21 

63.64 

72.93 

63.96 

72.65 

64.27 

72.37 

64.59 

97 

l 98 

73.96 

64.29 

73.68 

64.62 

73.40 

64.94 

73.11 

65.26 

98 

l 99 

74.72 

64.95 

74.43 

65.28 

74.15 

65.60 | 

73.86 

65.92 

99 

1100 

75.47 

65.61 

75.18 

65.93 

74.90 

66.26 

74.61 

66.59 

j. 

100 

I p 

II 9 

Dep. j 

Lat. 

Dep. 

Lat. 

Dep. 1 

Lat. 

Dep. 

Lat. 

c> 

o 

a 

1 <“• 

1 ^ 

1 **-* 

1 (/J 
'if I • M 

ll Q 

49 Deg. 

48f Deg. 

48£ Deg. 

48} Deg. 

m 

• r-H 

Q 















































































































86 


TRAVERSE TABLE 


Distance. 

42 Deg. 

1 

42$ Deg. 

42* Deg. 

42| Deg. 

1 

V 

S3 

o 

? 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

1 

0.74 

0.67 

0.74 

0.67 

0.74 

0.68 

0.73 

0.68 

1 

2 

1.49 

1.34 

1.48 

1.34 

1.47 

1.35 

1.47 

1.36 

2 

3 

2.23 

2.01 

2.22 

2.02 

2.21 

2.03 

2.20 

2.04 

3 

4 

2.97 

2.68 

2.96 

2.69 

2.95 

2.70 

2.94 

2.72 

4 

5 

3.72 

3.35 

3.70 

3.36 

3.69 

3.38 

3.67 

3.39 

5 

6 

4.46 

4.01 

4.44 

4.03 

4.42 

4.05 

4.41 

4.07 

6 

7 

5.20 

4.68 

5.18 

4.71 

5.16 

4.73 

5.14 

4.75 

7 

8 

5.95 

5.35 

5.92 

5.38 

5.90 

5.40 

5.87 

5.43 

8 

9 

6.69 

6.02 

6.66 

6.05 

6.64 

6.08 

6.61 

6.11 

9 

10 

7.43 

6.69 

7 -40 

6.72 

7.37 

6.76 

7.34 

6.79 

10 

11 

8.17 

7.36 

8.14 

7.40 

8.11 

7.43 

8.08 

7.47 

11 

12 

8.92 

8.03 

8.88 

8.07 

8.85 

8.11 

8.81 

8.15 

12 

13 

9.66 

8.70 

9.62 

8.74 

9.58 

8.78 

9.55 

8.82 

13 

14 

10.40 

9.37 

10.36 

9.41 

10.32 

9.46 

10.28 

9.50 

14 

15 

11.15 

10.04 

11.10 

10.09 

11.06 

10.13 

11.01 

10.18 

15 

16 

11.89 

10.71 

11.84 

10.76 

11.80 

10.81 

11.75 

10.86 

16 

17 

12.63 

11.38 

12.58 

11.43 

12.53 

11.48 

12.48 

11.54 

17 

18 

13.38 

12.04 

13.32 

12.10 

13.27 

12.16 

13.22 

12.22 

18 

19 

14.12 

12.71 

14.06 

12.77 

14.01 

12.84 

13.95 

12.90 

19 

20 

14.86 

13.38 

14.80 

13.45 

14.75 

13.51 

14.69 

13.58 

20 

21 

15.61 

14.05 

15.54 

14.12 

15.48 

14.19 

15.42 

14.25 

21 

22 

16.35 

14.72 

16.28 

14.79 

16.22 

14.86 

16.16 

14.93 

22 

23 

17.09 

15.39 

17.02 

15.46 

16.96 

15.54 

16.89 

15.61 

23 

24 

17.84 

16.06 

17.77 

16.14 

17.69 

16.21 

17.62 

16.29 

24 

25 

18.58 

16.73 

18.51 

16.81 

18.43 

16.89 

18.36 

16.97 

25 

26 

19.32 

17.40 

19.25 

17.48 

19.17 

17.57 

19.09 

17.65 

26 

27 

20.06 

18.07 

19.99 

18.15 

19.91 

18.24 

19.83 

18.33 

27 

28 

20.81 

18.74 

20.73 

18.83 

20.64 

18.92 

20.56 

19.01 

28 

29 

21.55 

19.40 

21.47 

19.50 

21.38 

19.59 

21.30 

19.69 

29 

30 

22.29 

20.07 

22.21 

20.17 

22.12 

20.27 

22.03 

20.36 

30 

31 

23.04 

20.74 

22.95 

20.84 

22.86 

20.94 

22.76 

21.04 

31 

32 

23.78 

21.41 

23.69 

21.52 

23.59 

21.62 

23.50 

21.72 

32 

33 

24.52 

22.08 

24.43 

22.19 

24.33 

22.29 

24.23 

22.40 

33 

34 

25.27 

22.75 

25.17 

22.86 

25.07 

22.97 

24.97 

23.08 

34 

35 

26.01 

23.42 

25.91 

23.53 

25.80 

23.65 

25.70 

23.76 

35 

36 

26.75 

24.09 

26.65 

24.21 

26.54 

24.32 

26.44 

24.44 

36 

37 

27.50 

24.76 

27.39 

24.88 

27.28 

25.00 

27.17 

25.12 

37 

38 

28.24 

25.43 

28.13 

25.55 

28.02 

25.67 

27.90 

25.79 

38 

39 

28.98 

26.10 

28.87 

26.22 

28.75 

26.35 

28.64 

26.47 

39 

40 

29.73 

26.77 

29.61 

26.89 

29.49 

27.02 

29.37 

27.15 

40 

41 

30.47 

27.43 

30.35 

27.57 

30.23 

27.70 

30.11 

27.83 

41 

42 

31.21 

28.10 

31.09 

28.24 

30.97 

28.37 

30.84 

28.51 

42 

43 

31.96 

28.77 

31.83 

28.91 

31.70 

29.05 

31.58 

29.19 

43 

44 

32.70 

29.44 

32.57 

29.58 

32.44 

29.73 

32.31 

29.87 

44 

45 

33.44 

30.11 

33.31 

30.26 

33.18 

30.40 

33.04 

30.55 

45 

46 

34.18 

30.78 

34.05 

30.93 

33.91 

31.08 

33.78 

31.22 

46 

47 

34.93 

31.45 

34.79 

31.60 

34.65 

31.75 

34.51 

31.90 

47 

48 

35.67 

32.12 

35.53 

32.27 

35.39 

32.43 

35.25 

32.58 

48 

49 

36.41 

32.79 

36.27 

32.95 

36.13 

33.10 

35.98 

33.26 

49 

50 

37.16 

33.46 

37.01 

33.62 

36.86 

33.78 

36.72 

33.94 

50 

Distance. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Distance. 

48 Deg. 

47$ Deg. 

47* Deg. 

47$ Deg. 

~ r ’ r " " 1 1 1 





































































TRAVERSE TABLE. 


07 


Distance. 

42 Deg. 

42^ Deg. 

42£ Deg. 

42f Deg. j 

Distance. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

51 

37.90 

34.13 

37.75 

34.29 

37.60 

34.46 

37.45 

34.62 

51 

52 

38.64 

34.79 

38.49 

34.96 

38.34 

35.13 

38.18 

35.30 

52 

53 

39.39 

35.46 

39.23 

35.64 

39.08 

35.81 

38.92 

35.98 

53 

54 

40.13 

36.13 

39.97 

36.31 

39.81 

36.48 

39.65 

36.66 

54 

55 

40.87 

36.80 

40.71 

36.98 

40.55 

37.16 

40.39 

37.33 

55 

56 

41.62 

37.47 

41.45 

37.65 

41.29 

37.83 

41.12 

38.01 

56 

57 

42.36 

38.14 

42.19 

38.32 

42.02 

38.51 

41.86 

38.69 

57 

58 

43.10 

38.81 

42.93 

39.00 

42.76 

39.18 

42.59 

39.37 

58 

59 

43.85 

39.48 

43.67 

39.67 

43.50 

39.86 

43.32 

40.05 

59 

60 

44.59 

40.15 

44.41 

40.34 

44.24 

40.54 

44.06 

40.73 

60 

61 

45.33 

40.82 

45.15 

41.01 

44.97 

41.21 

44.79 

41.41 

61 

62 

46.07 

41.49 

45.89 

41.69 

45.71 

41.89 

45.53 

42.09 

62 

63 

46.82 

42.16 

46.63 

42.36 

46.45 

42.56 

46.26 

42.76 

63 

64 

47.56 

42.82 

47.37 

43.03 

47.19 

43.24 

47.00 

43.44 

64 

65 

48.30 

43.49 

48.11 

43.70 

47.92 

43.91 

47.73 

44.12 

65 

66 

49.05 

44.16 

48.85 

44.38 

48.66 

44.59 

48.47 

44.80 

66 

67 

49.79 

44.83 

49.59 

45.05 

49.40 

45.26 

49.20 

45.48 

67 

68 

50.53 

45.50 

50.33 

45.72 

50.13 

45.94 

49.93 

46.16 

68 

69 

51.28 

46.17 

51.07 

46.39 

50.87 

46.62 

50.67 

46.84 

69 

70 

52.02 

46.84 

51.82 

47.07 

51.61 

47.29 

51.40 

47.52 

70 

71 

52.76 

47.51 

52.56 

47.74 

52.35 

47.97 

52.14 

48.19 

71 

72 

53.51 

48.18 

53.30 

48.41 

53.08 

48.64 

52.87 

48.87 

72 

73 

54.25 

48.85 

54.04 

49.08 

53.82 

49.32 

53.61 

49.55 

73 

74 

54.99 

49.52 

54.78 

49.76 

54.56 

49.99 

54.34 

50.23 

74 

75 

55.74 

50.18 

55.52 

50.43 

55.30 

50.67 

55.07 

50.91 

75 

76 

56.48 

50.85 

56.26 

51.10 

56.03 

51.34 

55.81 

51.59 

76 

77 

57.22 

51.52 

57.00 

51.77 

56.77 

52.02 

56.54 

52.27 

77 

78 

57.97 

52.19 

57.74 

52.44 

57.51 

52.70 

57.28 

52.95 

78 

79 

58.71 

52.86 

58.48 

53.12 

58.24 

53.37 

58.01 

53.63 

79 

80 

59.45 

53.53 

59.22 

53.79 

58.98 

54.05 

58.75 

54.30 

80 

81 

60.19 

54.20 

59.96 

54.46 

59.72 

54.72 

59.48 

54.98 

81 

82 

60.94 

54.87 

60.70 

55.13 

60.46 

55.40 

60.21 

55.66 

82 

83 

61.68 

55.54 

61.44 

55.81 

61.19 

56.07 

60.95 

56.34 

83 

84 

62.42 

56.21 

62.18 

56.48 

61.93 

56.75 

61.68 

57.02 

84 

85 

63.17 

56.88 

62.92 

57.15 

62.67 

57.43 

62.42 

57.70 

85 

86 

63.91 

57.55 

63.66 

57.82 

63.41 

58.10 

63.15 

58.38 

86 

87 

64.65 

58.21 

64.40 

58.50 

64.14 

58.78 

63.89 

59.06 

87 

88 

65.40 

58.88 

65.14 

59.17 

64.88 

59.45 

64.62 

59.73 

83 

89 

66.14 

59.55 

65.88 

59.84 

65.62 

60.13 

65.35 

60.41 

89 

90 

66.88 

60.22 

66.62 

60.51 

66.35 

60.80 

66.09 

61.09 

90 

91 

67.63 

60.89 

67.36 

61.19 

67.09 

61.48 

66.82 

61.77 

91 

92 

68.37 

61.56 

68.10 

61.86 

67.83 

62.15 

67.56 

62.45 

92 

93 

69.11 

62.23 

68.84 

62.53 

68.57 

62.83 

68.29 

63.13 

93 

94 

69.86 

62.90 

69.58 

63.20 

69.30 

63.51 

69.03 

63.81 

94 

95 

70.60 

63.57 

70.32 

63.87 

70.04 

64.18 

69.76 

64.49 

95 

96 

71.34 

64.24 

71.06 

64.55 

70.78 

64.86 

70.49 

65.16 

96 

97 

72.08 

64.91 

71.80 

65.22 

71.52 

65.53 

71.23 

65.84 

97 

98 

72.83 

65.57 

72.54 

65.89 

72.25 

66.21 

71.96 

66.52 

98 

99 

73.57 

66.24 

73.28 

66.56 

72.99 

66.88 

72.70 

67.20 

99 

100 

74.31. 

66.91 

74.02 

67.24 

73.73 

67.56 

73.43 

67.88 

100 

• 

cu 

V 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

<v 

g 

*-> 

m 

• --i 

■Q 

48 Deg. 

471 Deg. 

47* Deg. 

47* Deg. 

et 

.2 

Q 




















































































TRAVERSE TABLE 


00 


d 

r n 
<-► 

V> 

3 

O 

43 Deg. 

43* Deg. 

43* Deg. 

43J Deg. 

Distance. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

j i 

0.73 

0.68 

0.73 

0.69 

0.73 

0.69 

0.72 

0.69 

1 

2 

1.46 

1.36 

1.46 

1.37 

1.45 

1.38 

1.44 

1.38 

2 

3 

2.19 

2.05 

2.19 

2.06 

2.18 

2.07 

2.17 

2.07 

3 

4 

2.93 

2.73 

2.91 

2.74 

2.90 

2.75 

2.89 

2.77 

4 

5 

3.66 

3.41 

3.64 

3.43 

- 3.63 

3.44 

3.61 

3.46 

5 

6 

4.39 

4.09 

4.37 

4.11 

4.35 

4.13 

4.33 

4.15 

6 

7 

5.12 

4.77 

5.10 

4.80 

5.08 

4.82 

5.06 

4.84 

7 

8 

5.85 

5.46 

5.83 

5.48 

5.80 

5.51 

5.78 

5.53 

8 

9 

6.58 

6.14 

6.56 

6.17 

6.53 

6.20 

6.50 

6.22 

9 

10 

7.31 

6.82 

7.28 

6.85 

7.25 

6.88 

7.22 

6.92 

10 

11 

8.04 

7.50 

8.01 

7.54 

7.98 

7.57 

7.95 

7.61 

11 

12 

8.78 

8.18 

8.74 

8.22 

8.70 

8.26 

8.67 

8.30 

12 

13 

9.51 

8.87 

9.47 

8.91 

9.43 

8.95 

9.39 

8.09 

13 

14 

10.24 

9.55 

10.20 

9.59 

10.16 

9.64 

10.11 

9.68 

14 1 

15 

10.97 

10.23 

10.93 

10.28 

10.88 

10.33 

10.84 

10.37 

15 

16 

11.70 

10.91 

11.65 

10.96 

11.61 

11.01 

11.56 

11.06 

16 ' 

17 

12.43 

11.59 

12.38 

11.65 

12.33 

11.70 

/12.28 

11.76 

17 

18 

13.16 

12.28 

13.11 

12.33 

13.06 

12.39 

13.00 

12.45 

18 

19 

13.90 

12.96 

13.84 

13.02 

13.78 

13.08 

13.72 

13.14 

19 ! 

20 

14.63 

13.64 

14.57 

13.70 

14.51 

13.77 

14.45 

13.83 

20 ; 

21 

15.36 

14.32 

15.30 

14.39 

15.23 

14.46 

15.17 

14.52 

21 

22 

16.09 

15.00 

16.02 

15.07 

15.96 

15.14 

15.89 

15.21 

22 i 

23 

16.82 

15.69 

16.75 

15.76 

16.68 

15.83 

16.61 

15.90 

23 

24 

17.55 

16.37 

17.48 

16.44 

17.41 

16.52 

17.34 

16.60 

24 

25 

18.28 

17.05 

18.21 

17.13 

18.13 

17.21 

18.06 

17.29 

25 1 

26 

19.02 

17.73 

18.94 

17.81 

18.86 

17.90 

18.78 

17.98 

26 

27 

19.75 

18.41 

19.67 

18.50 

19.59 

18.59 

19.50 

18.67 

27 ! 

j 28 

20.48 

19.10 

20.39 

19.19 

20.31 

19.27 

20.23 

19.36 

28 

29 

21.21 

19.78 

21.12 

19.87 

21.04 

19.96 

20.95 

20.05 

29 ! 

30 

21.94 

20.46 

21.85 

20.56 

21.76 

20.65 

21.67 

20.75 

30 

31 

22.67 

21.14 

22.58 

21.24 

22.49 

21.34 

22.39 

21.44 

31 

32 

23.40 

21.82 

23.31 

21.93 

23.21 

22.03 

23.12 

22.13 

32 1 

33 

24.13 

22.51 

24.04 

22.61 

23.94 

22.72 

23.84 

22.82 

33 

34 

24.87 

23.19 

24.76 

23.30 

24.66 

23.40 

24.56 

23.51 

34 1 

35 

25.60 

23.87 

25.49 

23.98 

25.39 

24.09 

25.28 

24.20 

35 ! 

36 

26.33 

24.55 

26.22 

24.67 

26.11 

24.78 

26.01 

24.89 

36 1 

37 

27.06 

25.23 

26.95 

25.35 

26.84 

25.47 

26.73 

25.59 

37 

38 

27.79 

25.92 

27.68 

26.04 

27.56 

26.16 

27.45 

26.28 

38 

39 

28.52 

26.60 

28.41 

26.72 

28.29 

26.85 

28.17 

26.97 

39 

40 

29.25 

27.28 

29.13 

27.41 

29.01 

27.53 

28.89 

27.66 

40 

1 

41 

29.99 

27.96 

29.86 

28.09 

29.74 

28.22 

29.62 

28.35 

41 

42 

30.72 

28.64 

30.59 

28.78 

30.47 

28.91 

30.34 

29.04 

42 

43 

31.45 

29.33 

31.32 

29.46 

31.19 

29.60 

31.06 

29.74 

43 

44 

32.18 

30.01 

32.05 

30.15 

31.92 

30.29 

31.78 

30.43 

44 

45 

32.91 

30.69 

32.78 

30.83 

32.64 

30.98 

32.51 

31.12 

45 

46 

33.64 

31.37 

33.51 

31.52 

33.37 

31.66 

33.23 

31.81 

46 

47 

34.37 

32.05 

34.23 

32.20 

34.09 

32.35 

33.95 

32.50 

47 

48 

35.10 

32.74 

34.96 

32.89 

34.82 

33.04 1 

34.67 

33.19 

48 

49 

35.84 

33.42 

35.69 

33.57 

35.54 

33.73 

35.40 

33.88 

49 

50 

t- 

36.57 

34.10 

36.42 

34.26 

36.27 

34.42 

36.12 

34.58 

50 1 

• 

qj 

o 

£} 

Dep. 1 

Lat. 

Dep. | 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

i 

o 

Cj 

•If 

« 1 

47 Deg. 

46f Deg. 

46* Deg. 

46* Deg. 

w 

iS 

cn 

• pH 

Q 















































































TRAVERSE TABRE 


89 


« 


I U 

1 »—< • 

co 

| P 

1 f 3 

43 Deg. 

43i Deg. 

43^ Deg. 

43f Deg. 

G 

• 

CO 

t-*- 

p 

1 o 

; <6 

Lat. 

1 Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

p 

o 

CD 

1 51 

37.30 

1 34.78 

37.15 

34.94 

36.99 

35.11 

36.84 

35.27 

51 

1 52 

38.03 

35.46 

37.88 

35.63 

37.72 

35.79 

37.56 

35.96 

52 

1 53 

38.76 

36.15 

38.60 

36.31 

38.44 

36.48 

38.29 

36.65 

53 

54 

39.49 

36.83 

39.33 

37.00 

39.17 

37.17 

39.01 

37.34 

54 

55 

40.22 

37.51 

40.06 

37.69 

39.90 

37.86 

39.73 

38.03 

55 

56 

40.96 

38.19 

40.79 

38.37 

40.62 

38.55 

40.45 

38.72 

56 

57 

41.69 

38.87 

41.52 

39.06 

41.35 

39.24 

41.17 

39.42 

57 

58 

42.42 

39.56 

42.25 

39.74 

42.07 

39.92 

41.90 

40.11 

58 

1 59 

43.15 

40.24 

42.97 

40.43 

42.80 

40.61 

42.62 

40.80 

59 

I 60 

43.88 

40.92 

43.70 

41.11 

43.52 

41.30 

43.34 

41.49 

60 

1 61 

44.61 

1 41.60 

44.43 

41.80 

44.25 

41.99 

44.06 

42.18 

61 

62 

45.34 

42.28 

45.16 

42.48 

44.97 

42.68 

44.79 

42.87 

62 

l 63 

46.08 

42.97 

45.89 

43.17 

45.70 

43.37 

45.51 

43.57 

63 

64 

46.81 

43.65 

46.62 

43.85 

46.42 

44.05 

46.23 

44.26 

64 

65 

47.54 

44.33 

47.34 

44.54 

47.15 

44.74 

46.95 

44.95 

65 

66 

48.27 

45.01 

48.07 

45.22 

47.87 

45.43 

47.68 

45.64 

66 

67 

49.00 

45.69 

48.80 

45.91 

48.60 

46.12 

48.40 

46.33 

67 

I 68 

49.73 

46.38 

49.53 

46.59 

49.33 

46.81 

49.12 

47.02 

68 

1 69 

50.46 

47.06 

50.26 

47.28 

50.05 

47.50 

49.84 

47.71 

69 

70 

51.19 

[ 47.74 

50.99 

47.96 

50.78 

48.18 

50.57 

48.41 

70 

L 71 

51.93 

48.42 

51.71 

48.65 

51.50 

48.87 

51.29 

49.10 

71 

72 

52.66 

49.10 

52.44 

49.33 

52.23 

49.56 

52.01 

49.79 

72 

1 73 

53.39 

49.79 

53.17 

50.02 

52.95 

50.25 

52.73 

50.48 

73 

1 74 

54.12 

50.47 

53.90 

50.70 

53.68 

50.94 

53.45 

51.17 

74 

75 

54.85 

51.15 

54.63 

51.39 

54.40 

51,63 

54.18 

51.86 

75 

I 76 

55.58 

51.83 

55.36 

52.07 

55.13 

52.31 

54.90 

52.55 

76 

1 77 

56.31 

52.51 

56.08 

52.76 

55.85 

53.00 

55.62 

53.25 

77 

78 

57.05 

53.20 

56.81 

53.44 

56.58 

53.69 

56.34 

53.94 

78 

I 7 9 

57.78 

53.88 

57.54 

54.13 

57.30 

54.38 

57.07 

54.63 

79 

I 80 

58.51 

54.56 

58.27 

54.81 

58.03 

55.07 

57.79 

55.32 

80 

1 81 

59.24 

55.24 

59.00 

55.50 

58.76 

55.76 

58.51 

56.01 

81 

I 82 

59.97 

55.92 

59.73 

56.18 

59.48 

56.45 

59.23 

56.70 

82 

1 83 

60.70 

56.61 

60.45 

56.87 

60.21 

57.13 

59.96 

57.40 

83 

! 84 

61.43 

57.29 

61.18 

57.56 

60.93 

57.82 

60.68 

58.09 

84 

85 

62.17 

57.97 

61.91 

58.24 

61.66 

58.51 

61.40 

58.78 

85 

1 86 

62.90 

58.65 

62.64 

58.93 

62.38 

59.20 

62.12 

59.47 

86 

87 

63.63 

59.33 

63.37 

59.61 

63.11 

59.89 

62.85 

60.16 

87 

! 88 

64.36 

60.02 

64.10 

60.30 

63.83 

60.58 

63.57 

60.85 

88 

89 

65.09 

60.70 

64.82 

60.98 

64.56 

61.26 

64.29 

61.54 

89 

I 90 

65.82 

61.38 

65.55 

61.67 

65.28 

61.95 

65.01 

62.24 

90 

1 91 

66.55 

62.06 

66.28 

62.35 

66.01 

62.64 

65.74 

62.93 

91 

f 92 

67.28 

62.74 

67.01 

63.04 

66.73 

63.33 

66.46 

63.62 

92 

1 93 

68.02 

63.43 

67.74 

63.72 

67.46 

64.02 

67.18 

64.31 

93 

94 

68.75 

64.11 

68.47 

64.41 

68.19 

64.71 

67.90 

65.00 

94 

95 

69.48 

64.79 

69.20 

65.09 

68.91 

65.39 

68.62 

65.69 

95 

98 

70.21 

65.47 

69.92 

65.78 

69.64 

66.08 

69.35 

66.39 

96 

97 

70.94 

66.15 

70.65 

66.46 

70.36 

66.77 

70.07 

67.08 

97 

I 98 

71.67 

66.84 

71.37 

67.15 

71.09 

67.46 

70.79 

67.77 

98 

99 

72.40 

67.52 

72.11 

67.83 

71.81 

68.15 

71.51 

68.46 

99 

1100 

73.14 

68.20 

72.84 

68.52 j 

72.54 

68.84 

72.24 

69.15 1 

00 

1 ^ 

Dep. J 

Lat. 

Dep. 1 

Lat. | 

Dep. ! 

Lat. j 

Dep. 

Lat. 

• 

o 

a 

II <3 

1 ^ 

47 Deg. 

1 

| 

46| Deg. 

' 46JDeg. 

’! 

46-\ Deg. 

*5 

cn 

Q 

— 


M 






















































































































TRAVERSE TABLE, 


Distance. 

44 Deg. 

44^ Deg. 

44§ Deg. 

44f Deg. 

_- 

i 

45 Deg. ! 

I Distance. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

1 

0.72 

0.69 

0.72 

0.70 

0.71 

0.70 

0.71 

0.71 

0.71 

0.71 

1 

2 

1.44 

1.39 

1.43 

1.40 

1.43 

1.40 

1.42 

1.41 

1.41 

1.41 

2 

3 

2.16 

2.08 

2.15 

2.09 

2.14 

2.10 

2.13 

2.11 

2.12 

2.12 

3 

4 

2.88 

2.78 

2.87 

2.79 

2.85 

2.80 

2.84 

2.82 

2.83 

2.83 

4 

5 

3.60 

3.47 

3.58 

3.49 

3.57 

3.50 

3.55 

3.52 

3.54 

3.54 

5 

6 

4.32 

4.17 

4.30 

4.19 

4.28 

4.21 

4.26 

4.22 

4.24 

4.24 

6 

7 

5.04 

4.86 

5.01 

4.88 

4.99 

4.91 

4.97 

4.93 

4.95 

4.95 

7 

8 

5.75 

5.56 

5.73 

5.58 

5.71 

5.61 

5.68 

5.63 

5.66 

5.66 

8 

9 

6.47 

6.25 

6.45 

6.28 

6.42 

6.31 

6.39 

6.34 

6.36 

6.36 

9 

10 

7.19 

6.95 

7.16 

6.98 

7.13 

7.01 

7.10 

7.04 

7.07 

7.07 

10 

11 

7.91 

7.64 

7.88 

7.68 

7.85 

7.71 

7.81 

7.74 

7.78 

7.78 

11 

12 

8.63 

8.34 

8.60 

8.37 

8.56 

8.41 

8.52 

8.45 

8.49 

8.49 

12 

13 

9.35 

9.03 

9.31 

9.07 

9.27 

9.11 

9.23 

9.15 

9.19 

9.19 

13 

14 

10.07 

9.73 

10.03 

9.77 

9.99 

9.81 

9.94 

9.86 

9.90 

9.90 

14 

15 

10.79 

10.42 

10.74 

10.47 

10.70 

10.51 

10.65 

10.56 

10.61 

10.61 

15 

16 

11.51 

11.11 

11.46 

11.16 

11.41 

11.21 

11.36 

11.26 

11.31 

11.31 

16 

17 

12.23 

11.81 

12.18 

11.86 

12.13 

11.92 

12.07 

11.97 

12.02 

12.02 

17 

I 18 

12.95 

12.50 

12.89 

12.56 

12.84 

12.62 

12.78 

12.67 

12.73 

12.73 

18 

S 19 

13.67 

13.20 

13.61 

13.26 

13.55 

13.32 

13.49 

13.38 

13.43 

13.43 

19 

1 20 

14.39 

13.89 

14.33 

13.96 

14.26 

14.02 

14.20 

14.08 

14.14 

14.14 

20 

21 

15.11 

14.59 

15.04 

14.65 

14.98 

14.72 

14.91 

14.78 

14.85 

14.85 

21 

22 

15.83 

15.28 

15.76 

15.35 

15.69 

15.42 

15.62 

15.49 

15.56 

15.56 

22 

23 

16.54 

15.98 

16.47 

16.05! 

16.40 

16.12 

16.33 

16.19 

16.26 

16.26 

23 

24 

17.26 

16.67 

17.19 

16.75 i 

17.12 

16.82 

17.04 

16.90 

16.97 

16.97 

24 

25 

17.98 

17.37 

17.91 

17.44 

17.83 

17.52 

17.75 

17.60 

17.68 

17.68 

25 

26 

18.70 

18.06 

18.62 

18.14 

18.54 

18.22 

18.46 

18.30 

18.38 

18.38 

26 

27 

19.42 

18.76 

19.34 

18.84 

19.26 

18.92 

19.17 

19.01 

19.09 

19.09 

27 

28 

20.14 

19.45 

|20.06 

19.54 

19.97 

19.63; 

19.89 

19.71 

19.80 

19.80 

28 

29 

20.86 

20.15 

120.77 

20.24 

20.68 

20.33 

20.60 

20.42 

20.51 

20.51 

29 

30 

21.58 

20.84 

21.49 

20.93 

21.40 

21.03 

21.31121.12 

21.21 

21.21 

30 

31 

22.30 

21.53 

122.21 

21.63 

22.11 

21.73 

22.02 21.82 

21.92 

21.92 

31 

32 

23.02 

22.23 

22.92 

22.33 

22.82 

22.43 

22.7322.53 

22.63 

22.63 

32 

33 

23.74 

22.92 

23.64 

23.03 

23.54 

23.13 

23.44 

23.23 

23.33 

23.33 

33 

34 

24.46 

23.62 

24.35 

23.72 

24.25 

23.83 

24.15 

23.94 

24.04 

24.04 

34 

35 

25.18 

24.31 

25.07 

24.42 

24.96 

24.53 

24.86 

24.64 

24.75 

24.75 

35 

36 

25.90 

25.01 

25.79 

25.12 

25.68 

25.23 

25.57 

25.34 

25.46 

25.46 

36 

37 

26.62 

25.70 

26.50 

25.82 

26.39 

25.93 

26.28 

26.05 

26.16 

26.16 

37 

38 

27.33 

26.40 

27.22 

26.52 

27.10 

26.63 

26.99 

26.75 

26.87 

26.87 

38 

39 

28.05 

27.09 

27.94 

27.21 

27.82 

27.34 

27.70 

27.46 

27.58 

27.58 

39 

40 

28.77 

27.79 

28.65 

27.91 

28.53 

28.04 

28.41 

28.16 

28.28 

28.28 

40 

41 

29.49 

28.48 

29.37 

28.61 

29.24 

28.74 

29.12 

28.86 

28.99 

28.99 

'41 

42 

30.21 

29.18 

30.08 

29.31 

29.96 

29.44 

29.83 

29.57 

29.7C 

29.70 

42 

43 

30.95 

129.87 

30.80 

30.00 

30.67 

30.14 

30.54 

30.27 

30.41 

30.41 

43 

44 

31.65 

•30.56 

31.52 

30.70 

31.38 

30.84 

31.25 

30.98 

31.11 

31.11 

44 

45 

32.31 

3D 26 

32.23 

31.40 

32.1C 

31.54 

31.96 

31.68 

31.85 

>31.82 

45 

46 

33.09 

31.95 

32.95 

32.10 

32.81 

32.24 

32.61 

32.38 

32.58 

132.53 

46 

47 

33.81 

32.65 

33.61 

32.80 

33.52 

’32.94 

33.38 

33.09 

33.28 

33.23 

47 

48 

34.55 

133.34 

34.38 

33.49 

34.24 

33.64 

34.08 

>33.79 

33.9^ 

133.94 

48 

, 49 

35.2/ 

34.04 

35.1C 

134.19 

34.95 

34.34 

34.8C 

>34.50 

34.6/ 

.34.65 

49 

50 

35.9' 

“34.73 

35.85 

>34.89 

35.66 

135.05 

35.51 

35.20 

35.3C 

5 35.36 

50 

« 

o 

a 

CO 

3 

Dep. 

Lat. 

Dep. 

— 

Lat. 

Dep. 

| Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Distance. 

46 Deg. 

451 Deg. 

! 45i Deg. 

II 

45$ Deg. 

45 Deg. 















































































































































TRAVERSE TABLE 


91 


e 
►— # 

OD 

P 

s 

o 

» 

44 Deg. 

44-| Deg. 

44£ Deg. 

44J Deg. 

45 Deg. 

O 

CO 

«-*■ 

P 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

B 

O 

a 

51 

36.69 

35.43 

36.53 

35.59 

36.38 

35.75 

36.22 

35.90 

36.06 

36.06 

51 

52 

37.41 

36.12 

37.25 

36.29 

37.09 

36.45 

36.93 

36.61 

36.77 

36.77 

52 

53 

38.12 

36.82 

37.96 

36.98 

37.80 

37.15 

37.64 

37.31 

37.48 

37.48 

53 

54 

38.84 

37.51 

38.68 

37.68 

38.52 

37.85 

38.35 

38.02 

38.18 

38.18 

54 

55 

39.56 

38.21 

39.40 

38.38 

39.23 

38.55- 

39.06 

38.72 

38.89 

38.89 

55 

56 

40.28 

38.90 

40.11 

39.03 

39.94 

39.25 

39.77 

39.42 

39.60 

39.60 

56 

57 

41.00 

39.60 

40.83 

39.77 

40.66 

39.95 

40.48 

40.13 

40.31 

40.31 

57 

58 

41.72 

40.29 

41.55 

40.47 

41.37 

40.65 

41.19 

40.83 

41.01 

41.01 

58 

59 

42.44 

40.98 

42.26 

41.17 

42.08 

41.35 

41.90 

41.54 

41.72 

41.72 

59 

60 

43.16 

41.68 

42.98 

41.87 

42.79 

42.05 

42.61 

42.24 

42.43 

42.43 

60 

61 

43.88 

42.37 

43.69 

42.57 

43.51 

42.76 

43.32 

42.94 

43.13 

43.13 

61 

62 

44.60 

43.07 

44.41 

43.26 

44.22 

43.46 

44.03 

43.65 

43.84 

43.84 

62 

63 

45.32 

43.76 

45.13 

43.96 

44.93 

44.16 

44.74 

44.35 

44.55 

44.55 

63 

64 

46.04 

44.46 

45.84 

44.66 

45.65 

44.86 

45.45 

45.06 

45.25 

45.25 

64 

65 

46.76 

45.15 

46.56 

45.36 

46.36 

45.56 

46.16 

45.76 

45.96 

45.96 

65 

66 

47.48 

45.85 

47.28 

46.05 

47.07 

46.26 

46.87 

46.46 

46.67 

46.67 

66 

67 

48.20 

46.54 

47.99 

46.75 

47.79 

46.96 

47.58 

47.17 

47.38 

47.38 

67 

68 

48.92 

47.24 

48.71 

47.45 

48.50 

47.66 

48.29 

47.87 

48.08 

48.08 

68 

69 

49.63 

47.93 

49.42 

48.15 

49.21 

48.36 

49.00 

48.58 

48.79 

48.79 

69 

70 

50.35 

48.63 

50.14 

48.85 

49.93 

49.06 

49.71 

49.28 

49.50 

49.50 

70 

71 

51.07 

49.32 

50*86 

49.54 

50.64 

49.76 

50.42 

49.98 

50.20 

50.20 

71 

72 

51.79 

50.02 

51.57 

50.24 

51.35 

50.47 

51.13 

50.69 

50.91 

50.91 

72 

73 

52.51 

50.71 

52.29 

50.94 

52.07 

51.17 

51.84 

51.39 

51.62 

51.62 

73 

74 

53.23 

51.40 

53.01 

51.64 

52.78 

51.87 

52.55 

52.10 

52.33 

52.33 

74 

75 

53.95 

52.10 

53.72 

52.33 

53.49 

52.57 

53.26 

52.80 

53.03 

53.03 

75 

76 

54.67 

52.79 

54.44 

53.03 

54.21 

53.27 

53.97 

53.51 

53.74 

53.74 

76 

77 

55.39 

53.49 

55.16 

53.73 

54.92 

53.97 

54.68 

54.21 

54.45 

54.45 

77 

78 

56.11 

54.18 

55.87 

54.43 

55.63 

54.67 

55.39 

54.91 

55.15 

55.15 

78 

79 

56.83 

54.88 

56.59 

55.13 

56.35 

55.37 

56.10 

55.62 

55.86 

55.86 

79 

80 

57.55 

55.57 

57.30 

55.82 

57.06 

56.07 

56.81 

56.32 

56.57 

56.57 

80 

81 

58.27 

56.27 

58.02 

56.52 

57.77 

56.77 

57.52 

57.03 

57.28 

57.28 

81 

82 

58.99 

56.96 

58.74 

57.22 

58.49 

57.47 

58.24 

57.73 

57.98 

57.98 

82 

83 

59.71 

57.66 

59.45 

57.92 

59.20 

58.18 

58.95 

58.43 

58.69 

58.69 

83 

84 

60.42 

58.35 

60.17 

58.61 

59.91 

58.88 

59.66 

59.14 

59.40 

59.40 

84 

85 

61.14 

59.05 

60.89 

59.31 

60.63 

59-58 

60.37 

59.84 

60.10 

60.10 

85 

86 

61.86 

59.74 

61.60 

60.01 

61.34 

60.28 

61.08 

60.55 

60.81 

60.81 

86 

87 

62.58 

60.44 

62.32 

60.71 

62.05 

60.98 

61.79 

61.25 

61.52 

61.52 

87 

88 

63.30 

61.13 

63.03 

61.41 

62.77 

61.68 

62.50 

61.95 

62.23 

62.23 

88 

89 

64.02 

61.82 

63.75 

62.10 

63.48 

62.38 

63.21 

62.66 

62.93 

62.93 

89 

90 

64.74 

62.52 

64.47 

62.80 

64.19 

63.08 

63.92 

63.36 

63.64 

63.64 

90 

91 

65.46 

63.21 

65.18 

63.50 

64.91 

63.78 

64.63 

64.07 

64.35 

64.35 

91 

92 

66.18 

63.91 

65.90 

64.20 

65.62 

64.48 

65.34 

64.77 

65.05 

65.05 

92 

93 

66.90 

64.60 

66.62 

64.89 

66.33 

65.18 

66.05 

65.47 

65.76 

65.76 

93 

94 

67.62 

65.30 

67.33 

65.59 

67.05 

65.89 

66,76 

66.18 

66.47 

66.47 

94 

95 

68.34 

65.99 

68.05 

66.29 

67.76 

66.59 

67.47 

66.88 

67.18 

67.18 

95 

96 

69.06 

66.69 

68.76 

66.99 

68.47 

67.29 

68.18 

67.59 

67.88 

67.88 

96 

97 

69.78 

67.38 

69.48 

67.69 

69.19 

67.99 

68.89 

68.29 

68.59 

68.59 

97 

98 

70.50 

68.08 

70.20 

68.38 

69.90 

68.69 

69.60 

68.99 

69.30 

69.30 

98 

99 

71.21 

68.77 

70.91 

69.08 

70.61 

69.39 

70.31 

69.70 

70.00 

70.00 

99 

100 

71.93 

69.47 

71.63 

69.78 

71.33 

70.09 

71.02 

70.40 

70.71 

70.71 

100 

p 

o 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

aj 

0 

a 

c 

a 

73 

Q 

46 Deg. 

45f Deg. 

45$ Deg. 

45i Deg. 

1 

45 Deg. 

a 

0 n 

* ^ 

0 
























































































A TABLE 


OF 


LOGARITHMS, 


FROM 1 TO 10,000. 


Note. The index of the logarithm of every integer 

w 

number consisting of only one figure is 0, of two figures 
1, of three figures 2, of four figures 3; being always a 
unit less than the number of figures contained in the 
integer number. In this table, as is generally the case, 
the index to the logarithm of every number above 100 is 
omitted; yet in the operation must be prefixed according 
to this remark; so the logarithm of 700 is 2,84510, and 
of 7000 is 3,84510, and so of the rest. 


No. 

Log. 

No. 

Log. 

No. 

Log. 

No. 

Log. 

No. 

Log. 

1 

0.00000 

21 

1.32222 

41 

1.61278 

61 

1.78533 

81 

1.90849 

2 

0.30103 

22 

1.34242 

42 

1.62325 

62 

1.79239 

82 

1.91381 

3 

0.47712 

23 

1.36173 

43 

1.63347 

63 

1.79934 

83 

1.91908 

4 

0.60206 

24, 

1.38021 

44 

1.64345 

64 

1.80618 

84 

1.92428 

5 

0.69897 

25 

1.39794 

45 

1.65321 

65 

1.81291 

85 

1.§2942 

6 

0.77815 

26 

1.41497 

46 

1.66276 

66 

1.81954 

86 

1.93450 

7 

0.84510 

27 

1.43136 

47 

1.67210 

67 

1.82607 

87 

1.93952 

8 

0.90309 

28 

1.44716 

48 

1.68124 

68 

1.83251 

88 

1.94448 

9 

0.95424 

29 

1.46240 

49 

1.69020 

69 

1.83885 

89 

1.94939 

10 

1.00000 

30 

1.47712 

50 

1.69897 

70 

1.84510 

90 

1.95424 

11 

1.04139 

31 

1.49136 

51 

1.70757 

71 

1.85126 

91 

1.95904 

12 

1.07918 

32 

1.50515 

52 

1.71600 

72 

1.85733 

92 

1.96379 

13 

1.11394 

33 

1.51851 

53 

1.72428 

73 

1.86332 

93 

1.96848 

14 

1.14613 

34 

1.53148 

54 

1.73239 

74 

1.86923 

94 

1.97313 

15 

1.17609 

35 

36 

1.54407 

55 

1.74036 

75 

1.87506 

95 

1.97772 

16 

1.20412 

1.55630 

56 

1.74819 

76 

1.88081 

96 

1.98227 

17 

1.23045 

37 

1.56820 

57 

1.75587 

77 

1.88649 

97 

1.98677 

18 

1.25527 

38 

1.57978 

58 

1.76343 

78 

1.89209 

98 

1.99123 

19 

1.27875 

39 

1.59106 

59 

1.77085 

79 

1.89763 

99 

1.99564 

20 

1.30103 

40 

1.60206 

60 

1.77815 

80 

1.90309 

100 

2.00000 
























Logarithms from 1 to 10,000. 93 


No. 

0 

1 

2 

3 

4 

5 

6 

7 

’ 8 

9 

100 

00000 

00043 

00087 

00130 

00173 

00217 

00260 

00303 

00346 

00389 

101 

00432 

00475 

00518 

00561 

00604 

00647 

00689 

00732 

00775 

00817 

102 

00860 

00903 

00945 

00988 

01030 

01072 

01115 

01157 

01199 

01242 

103 

01284 

01326 

01368 

01410 

01452 

01494 

01536 

01578 

01620 

01662 

104 

01703 

01745 

01787 

01828 

01870 

01912 

01953 

01995 

02036 

02078 

105 

02119 

02160' 

152202 

02243 

02284 

02325 

02366 

02407 

02449 

02490 

106 

02531 

02572 

02612 

02653 

02694 

02735 

02776 

02816 

02857 

02898 

107 

02938 

02979 

03019 

03060 

03100 

03141 

03181 

03222 

03262 

03302 

108 

03342 

03383 

03423 

03463 

03503 

03543 

03583 

03623 

65St)3 

03703 

109 

03743 

03782 

03822 

03862 

03902 

03941 

03981 

04021 

04060 

04100 

110 

04139 

04179 

04218 

04258 

04297 

04336 

04376 

04415 

04454 

04493 

111 

04532 

04571 

04610 

04650 

04689 

04727 

04766 

04805 

04844 

04883 

112 

04922 

0496?' 

04999 

05038 

05077 

05115 

05154 

05192 

05231 

05269 

113 

05308 

05346 

05385 

05423 

05461 

05500 

05538 

05576 

05614 

05652 

114 

05690 

05729 

05767 

05805 

05843 

05881 

05918 

05956 

05994 

06032 

115 

06070 

06108 

06145 

06183 

06221 

06258 

06296 

06333 

06371 

06408 

116 

06446 

06483 

06521 

06558 

06595 

06633 

06670 

06707 

06744 

06781 

117 

06819 

06856 

06893 

06930 

06967 

07004 

07041 

07078 

07115 

07151 

118 

07188 

07225 

07262 

07298 

07335 

07372 

07408 

07445 

07482 

07518 

119 

07555 

07591 

07628 

' 

07664 

07700 

07737 

07773 

07809 

07846 

07882 

120 

07918 

07954 

07990 

08027 

08063 

08099 

08135 

08171 

08207 

08243 

121 

08279 

08314 

08350 

08386 

08422 

08458 

08493 

08529 

08565 

08600 

122 

08636 

08672 

08707 

08743 

08778 

08814 

08849 

08884 

08920 

08955 

123 

08991 

09026 

09061 

09096 

09132 

09167 

09202 

09237 

09272 

09307 

124 

09342 

09377 

09412 

09447 

09482 

09517 

09552 

09587 

09621 

09656 

1.25 

09691 

09726 

09760 

09795 

09830 

09864 

09899 

09934 

09968 

10003 

126 

10037 

10072 

10106 

10140 

10175 

10209 

10243 

10278 

10312 

10346 

127 

10380 

104151 

10449 

10483 

10517 

10551 

10585 

10619 

10653 

10687 

128 

10721 

10 755 

10789 

10823 

10857 

10890 

10924 

10958 

10992 

11025 

129 

11059 

11093 

11126 

11160 

11193 

11227 

11261 

11294 

113^7 

11361 

130 

11394 

11428 

11461 

11494 

11528 

11561 

11594 

11628 

11661 

11694 

131 

11727 

11760 

11793 

11826 

11860 

11893 

11926 

11959 

11992 

12024 

132 

12057 

12090 

12123 

12156 

12189 

12222 

12254 

12287 

12320 

12352 

133 

12385 

12418< 

12450 

12483 

12516 

12548 

12581 

12613 

12646 

12678 

134 

12710 

12743 

12775 

12808 

12840 

12872 

12905 

12937 

12969 

13001 

135 

13033 

13066 

13098 

13130 

13162 

13194 

13226 

13258 

13290 

13322 

136 

13354 

13386 

13418 

13450 

13481 

13513 

13545 

13577 

13609 

13640 

137 

13672 

13704 

13735 

13767 

13799 

13830 

13862 

13893 

13925 

13956 

138 

13988 

14019 

14051 

14082 

14114 

14145 

14176 

14208 

14239 

14270 

139 

14301 

14333 

14364 

14395 

14426 

14457 

14489 

14520 

14551 

14582 

140 

14613 

14644 

14675 

14706 

14737 

14768 

14799 

14829 

14860 

14891 

141 

14922 

14953 

14983 

15014 

15045 

15076 

15106 

15137 

15168 

15198 

142 

15229 

15259 

15290 

15320 

15351 

15381 

15412 

15442 

15473 

15503 

143 

15534 

15564 

15594 

15625 

15655 

15685 

15715 

15746 

15776 

15806 

144 

15836 

15866 

15897 

15927 

15957 

15987 

16017 

16047 

16077 

16107 

145 

16137 

16167 

16197 

16227 

16256 

16286 

16316 

16346 

16376 

16406 

146 

16435 

16465 

16495 

16524 

16554 

16584 

16613 

16643 

16673 

16702 

147 

16732 

16761 

16791 

16820 

16850 

16879 

16909 

16938 

16967 

16997 

148 

17026' 

17056 

17085 

17114 

17143 

17173 

17202 

17231 

17260 

17289 

149 

17319 

17348 

17377 

17406 

17435 

17464 

17493 

17522 

17551 

17580 

150 

17609 

17638 

17667 

17696 

17725 

17754 

17782 

17811 

17840 

17869 

151 

17898 

17926 

17955 

17984 

18013 

18041 

18070 

18099 

18127 

18156 

152 

18184 

18213 

18241 

18270 

18298 

18327 

18355 

18384 

18412 

18441 

153 

18469 

18498 

18526 

18554 

18383 

18611 

18689 

18667 

18696 

18724 

' 154 

18752 

18780 

18808 

18837 

18865 

18893 

18921 

18949 

18977 

19005 

i 155 

19033 

19061 

19089 

19117 

19145 

19173 

19201 

19229 

19257 

19285 

156 

19312 

19340 

19368 

19396 

19424 

19451 

19479 

19507 

19535 

19562 

i 157 

19590 

19618 

19645 

19673 

19700 

19728 

19756 

19783 

19811 

19838 

158 

19866 

19893 

19921 

19948 

19976 

20003 

20030 

20058 

20085 

20112 

159 

20140 

20167 

20194 

20222 

20249 

20276 

20303 

20330 

20358 

20385 

































































































94 Logarithms from 1 to 10,000. 


No. 

0 

1 

2 

3 

4 

5 

6 

7 

8 

9 

160 

20412 

20439 

20466 

20493 

20520 

20548 

20575 

20602 

20629 

20656 

161 

20683 

20710 

20737 

20763 

20790 

20817 

20844 

20871 

20898 

20925 

162 

20952 

20978 

21005 

21032 

21059 

21085 

21112 

21139 

21165 

21192 

163 

21219 

21245 

21272 

21299 

21325 

21352 

21378 

21405 

21431 

21458 

164 

21484 

21511 

21537 

21564 

21590 

21617 

21643 

21669 

21696 

21722 

165 

21748 

21775 

21801 

21827 

21854 

21880 

21906 

21932 

21958 

21985 

166 

22011 

22037 

22063 

22089 

22115 

22141 

22167 

22194 

22220. 

22246 

167 

22272 

22298 

22324 

22350 

22376 

22401 

22427 

22453 

22479 

22505 

168 

2253*1- 

22557 

22583 

22608 

22634 

22660 

22686 

22712 

22737 

22763 

169 

22789 

22814 

22840 

22866 

22891 

22917 

22943 

22968 

22994 

23019 

170 

23045 

23070 

23096 

23121 

23147 

23172 

23198 

23223 

23249 

23274 

171 

23300 

23325 

23350 

23376 

23401 

23426 

23452 

23477 

23502 

23528 

172 

23553 

23578 

23603 

23629 

23654 

23679 

23704 

23729 

23754 

23779 

173 

23805 

23830 

23855 

23880 

23905 

23930 

23955 

23980 

24005 

24030 

174 

24055 

24080 

24105 

24130 

24155 

24180 

24204 

24229 

24254 

24279 

175 

24304 

24329 

24353 

24378 

24403 

24428 

24452 

24477 

24502 

24527 

176 

24551 

24576 

24601 

24625 

24650 

24674 

24699 

24724 

24748 

24773 

177 

24797 

24822 

24846 

24871 

24895 

24920 

24944 

24969 

24993 

25018 

178 

25042 

25066 

25091 

25115 

25139 

25164 

25188 

25212 

25237 

25261 

179 

25285 

25310 

25334 

25358 

25382 

25406 

25431 

25455 

25479 

25503 

180 

25527 

25551 

25575 

25600 

25624 

25648 

25672 

25696 

25720 

25744 

181 

25768 

25792 

25816 

25840 

25864 

25888 

25912 

25935 

25959 

25983 

132 

26007 

26031 

26055 

26079 

26102 

26126 

26150 

26174 

26198 

26221 

183 

26245 

26269 

26293 

26316 

26340 

26364 

26387 

26411 

26435 

26458 

134 

26482 

26505 

26529 

26553 

26576 

26600 

26623 

26647 

26670 

26694 

185 

26717 

26741 

26764 

26788 

26811 

26834 

26858 

26881 

26905 

26928 

186 

26951 

26975 

26998 

27021 

27045 

27068 

27091 

27114 

27138 

27161 

187 

27184 

27207 

27231 

27254 

27277 

27300 

27323 

27346 

2^7? 

27370 

27393 

188 

27416 

27439 

27462 

27485 

27508 

27531 

27554 

27600 

27623 

189 

27646 

27669 

27692 

27715 

27738 

27761 

27784 

27807 

27830 

27852 

190 

27875 

27898 

27921 

27944 

27967 

27989 

28012 

28035 

28058 

28081 

191 

23103 

28126 

28149 

28171 

28194 

28217 

28240 

28262 

28285 

28307 

192 

28330 

28353 

28375 

28398 

28421 

28443 

28466 

28488 

28511 

28533 

193 

28556 

28578 

28601 

28623 

28646 

28668 

28691 

28713 

28735 

28758 

194 

28780 

28803 

28825 

28847 

28870 

28892 

28914 

28937 

28959 

28981 

195 

29003 

29026 

29048 

29070 

29092 

29115 

29137 

29159 

29181 

29203 

196 

29226 

29248 

29270 

29292 

29314 

29336 

29358 

29380 

29403 

29425 

197 

29447 

29469 

29491 

29513 

29535 

29557 

29579 

29601 

29623 

29645 

198 

29667 

29688 

29710 

29732 

29754 

29776 

29798 

29820 

29842 

29863 

199 

29885 

29907 

29929 

29951 

29973 

29994 

30016 

30038 

30060 

30081 

200 

30103 

30125 

30146 

30168 

30190 

30211 

30233 

30255 

30276 

30298 

201 

30320 

30341 

30363 

30334 

30406 

30428 

30449 

30471 

30492 

30514 

202 

30535 

30557 

30578 

30600 

30621 

30643 

30664 

30685 

30707 

30728 

203 

30750 

30771 

30792 

30814 

30835 

30856 

30878 

30899 

30920 

30942 

204 

30963 

30984 

31006 

31027 

31048 

31069 

31091 

31112 

31133 

31154 

205 

31175 

31197 

31218 

31239 

31260 

31281 

31302 

31323 

31345 

31366 

206 

31387 

31408 

31429 

31450 

31471 

31492 

31513 

31534 

31555 

31576 

207 

31597 

31618 

31639 

31660 

31681 

31702 

31723 

31744 

31765 

31785 

208 

31806 

31827 

31848 

31869 

31890 

31911 

31931 

31952 

31973 

31994 

209 

32015 

32035 

32056 

32077 

32098 

32118 

32139 

32160 

32181 

32201 

210 

32222 

32243 

32263 

32284 

32305 

32325 

32346 

32366 

32387 

32408 

211 

*212 

32428 

32449 

32469 

32490 

32510 

32531 

32552 

32572 

32593 

32613 

32634 

32654 

32675 

32695 

32715 

32736 

32756 

32777 

32797 

32818 

213 

32838 

32858 

32879 

32899 

32919 

32940 

32960 

32980 

33001 

33021 

214 

33041 

33062 

33082 

33102 

33122 

33143 

33163 

33183 

33203 

33224 

215 

33244 

33264 

33284 

33304 

33325 

33345 

33365 

33385 

33405 

33425 

216 

33445 

33465 

33486 

33506 

33526 

33546 

33566 

33586 

33606 

33626 

217 

33646 

33666 

33686 

33706 

33726 

33746 

33766 

33786 

33806 

33826 

218 

33846 

33866 

33885 

33905 

33925 

33945 

33965 

33985 

34005 

34025 

219 

34044 

34064 

34084 

34104 

34124 

34143 

34163 

34183 

34203 

34223 




























































































05 


* 

Logarithms from 1 to 10,000. 


No. 

0 

1 

2 

3 

4 

5 

6 

7 

8 

9 

220 

34242 

34262 

34282 

34301 

34321 

34341 

34361 

34380 

34400 

34420 

221 

34439 

34459 

34479 

34498 

34518 

34537 

34557 

•34577 

34596 

34616 

222 

34635 

34655 

34674 

34694 

34713 

34733 

34753 

34772 

34792 

34811 

223 

34830 

34850 

34869 

34889 

34908 

34928 

34947 

34967 

34986 

35005 

224 

35025 

35044 

35064 

35083 

35102 

35122 

35141 

35160 

35180 

35199 

225 

35218 

35238 

35257 

35276 

35295 

3^315 

35334 

35353 

35372 

35392 

226, 

35411 

35430 

35449 

35468 

35488 

35507 

35526 

35545 

35564 

35583 

227 

35603 

35622 

35641 

35660 

35679 

35698 

35717 

35736 

35755 

35774 

228 

35793 

35813 

35832 

35851 

35870 

35889 

35908 

35927 

35946 

35965 

229 

35984 

36003 

36021 

36040 

36059 

36078 

36097 

36116 

36135 

36154 

230 

36173 

36192 

36211 

36229 

36248 

36267 

36286 

36305 

36324 

36342 

231 

36361 

36380 

36399 

36418 

36436 

36455 

36474 

36493 

36511 

26530 

232 

36549 

36568 

36586 

36605 

36624 

36642 

36661 

36680 

36698 

36717 

233 

36736 

36754 

36773 

36791 

36810 

36829 

36847 

36866 

36884 

36903 

234 

36922 

36940 

36959 

36977 

36996 

37014 

37033 

37051 

37070 

37088 

235 

37107 

37125 

37144 

37162 

37181 

37199 

37218 

37236 

37254 

37273 

236 

37291 

37310 

37328 

37346 

37365 

37383 

37401 

37420 

37438 

37457 

237 

37475 

37493 

37511 

37530 

37548 

37566 

37585 

37603 

37621 

37639 

238 

37658 

37676 

37694 

37712 

37731 

37749 

37767 

37785 

37803 

37822 

239 

37840 

37858 

37876 

37894 

37912 

37931 

37949 

37967 

37985 

38003 

240 

38021 

38039 

38057 

38075 

38093 

38112 

38130 

38148 

38166 

38184 

241 

38202 

38220 

38238 

38256 

38274 

38292 

38310 

38328 

38346 

38364 

242 

38382 

38399 

38417 

38435 

38453 

38471 

38489 

38507 

38525 

38543 

243 

38561 

38578 

38596 

38614 

38632 

38650 

3^668 

38686 

38703 

38721 

244 

38739 

38757 

38775 

38792 

38810 

38828 

38846 

38863 

38881 

38899 

245 

38917 

38934 

38952 

38970 

38937 

39005 

39023 

39041 

39058 

39076 

246 

39094 

39111 

39129 

39146 

39164 

39182 

39199 

39217 

39235 

39252 

247 

39270 

3920* 

39305 

39322 

39340 

39358 

39375 

39393 

39410 

39428 

248 

39445 

39463 

39480 

39498 

39515 

39533 

39550 

39568 

39585 

39602 

249 

39620 

39637 

39655 

39672 

39690 

39707 

39724 

39742 

39759 

39777 

250 

39794 

39811 

39829 

39846 

39863 

39881 

39898 

39915 

39933 

39950 

251 

39967 

39985 

40002 

40019 

40037 

40054 

40071 

40088 

40106 

40123 

252 

40140 

40157, 

4017.\ 

40192 

40209 

40226- 

40243 

40261 

40278 

40295 

253 

40312 

40329 

40346 

40364 

40381 

40398 

40415 

40432 

40449 

40466 

254 

40483 

40500 

40518 

40535 

40552 

40569 

40586 

40603 

40620 

40637 

255 

40654 

40671 

40688 

40705 

40722 

40739 

40756 

40773 

40790 

40807 

256 

40824 

40841 

40858 

40875 

40892 

40909 

40926 

40943 

40960 

40976 

257 

40993 

41010 

41027 

41044 

41061 

41078 

41095 

41111 

41128 

41145 

258 

41162 

41179 

41196 

41212 

41229 

41246 

41263 

41280 

41296 

41313 

259 

41330 

41347 

41363 

41380 

41397 

41414 

41430 

41447 

41464 

41481 

260 

41497 

41514 

41531 

41547 

41564 

41581 

41597 

41614 

41631 

41647 

261 

41664 

41681 

41697 

41714 

41731 

41747 

41764 

41780 

41797 

41814 

262 

41830 

41847 

41863 

41880 

41896 

41913 

41929 

41946 

41963 

41979 

263 

41996 

42012 

42029 

42045 

42062 

42078 

42095 

42111 

42127 

42144 

264 

42160 

42177 

42193 

42210 

42226 

42243 

42259 

42275 

42292 

42308 

265 

42325 

42341 

42357 

42374 

42390 

42406 

42423 

42439 

42455 

42472 

266 

42488 

42504 

42521 

42537 

42553 

42570 

42586 

42602 

42619 

42635 

267 

42651 

42667 

42684 

42700 

42716 

42732 

42749 

42765 

42781 

42797 

268 

42813 

42830 

42846 

42862 

42878 

42894 

42911 

42927 

42943 

42959 

269 

42975 

42991 

43008 

43024 

43040 

43056 

43072 

43088 

43104 

43120 

270 

43136 

43152 

43169 

43185 

43201 

43217 

43233 

43249 

43265 

43281 

271. 

43297 

43313 

43329 

43345 

43361 

43377 

43393 

43409 

43425 

43441 

272 

43457 

-43473 

43489 

43505 

43521 

43537 

43553 

43569 

43584 

43600 

273 

43616 

43632 

43648 

43664 

43680 

43696 

43712 

43727 

43743 

43759 

274 

43775 

43791 

43807 

43823 

43838 

43854 

43870 

43886 

43902 

43917 

275 

43933 

43949 

43965 

43981 

43996 

44012 

44028 

44044 

44059 

44075 

276 

44091 

44107 

44122 

44138 

44154 

44170 

44185 

44201 

44217 

44232 

277 

44248 

44264 

44279 

44295 

44311 

44326 

44342 

44358 

44373 

44389 

278 

44404 

44420 

44436 

44451 

44467 

44483 

44498 

44514 

44529 

44545 

279 

44560 

44576 

44592 

44607 

44623 

44638 

44654 

44669 

44685 

44*09 























































































96 




* 

Logarithms from 1 to 10,000. 


No. 

0 

1 

2 

3 

4 

5 

6 

7 

8 

9 

28 0 

44716 

44731 

44747 

44762 

44778 

44793 

44809 

44824 

44840 

44855 

281 

44871 

44886 

44902 

44917 

44932 

44948 

44963 

44979 

44994 

45010 

282 

45025 

45040' 

45056 

45071 

45086 

45102 

45117 

45133 

45148 

45163 

283 

45179 

45194 

45209 

45225 

45240 

45255 

45271 

45286 

45301 

45317 

284 

45332 

45347 

45362 

45378 

45393 

45408 

45423 

45439 

45454 

45469 

285 

45484 

45500 

45515 

45530 

45545 

45561 

45576 

45591 

45606 

45621 

286 

45637 

45652 

45667 

45682 

45697 

45712 

45728 

45743 

45758 

45773 

287 

45788 

45803 

45818 

45834 

45849 

45864 

45879 

45894 

45909 

45924 

288 

45939 

45954 

45969 

45984 

46000 

46015 

46030 

46045 

46060 

46075 

289 

46090 

46105 

46120 

46135 

46150 

46165 

46180 

46195 

46210 

46225 

290 

46240 

46255 

46270 

46285 

46300 

46315 

46330 

46345 

46359 

46374 

291 

46389 

46404 

46419 

46434 

46449 

46464 

46479 

46494 

46509 

46523 

292 

46538 

46553 

46568 

46583 

46598 

46613 

46627 

46642 

46657 

46672 

293 

46687 

46702 

46716 

46731 

46746 

46761 

46776 

46790 

46805 

46820 

294 

46835 

46850 

46864 

46879 

46894 

46909 

46923 

46938 

46953 

46967 

295 

46982 

46997 

47012 

47026 

47041 

47056 

47070 

47085 

47100 

47114 

296 

47129 

47144 

47159 

47173 

47188 

47202 

47217 

47232 

47246 

47261 

297 

47276 

47290 

47305 

47319 

47334 

47349 

47363 

47378 

47392 

47407 

298 

47422 

47436 

47451 

47465 

47480 

47494 

47509 

47524 

47538 

47553 

299 

47567 

47582 

47596 

47611 

47625 

47640 

47654 

47669 

47683 

47698 

300 

47712 

47727 

47741 

47756 

47770 

47784 

47799 

47813 

47828 

47842 

301 

47857 

47871 

47885 

47900 

47914 

47929 

47943 

47958 

47972 

47986 

302 

48001 

48015 

48029 

48044 

48058 

48073 

48087 

48101 

48116 

48130 

303 

48144 

48159 

48173 

48187 

48202 

48216 

48230 

48244 

48259 

48273 

304 

48287 

48302 

48316 

48330 

48344 

48359 

48373 

48387 

48401 

48416 

305 

48430 

48444 

48458 

48473 

48487 

48501 

48515 

48530 

48544 

48558 

306 

48572 

48586 

48601 

48615 

48629 

48643 

48657 

48671 

48686 

48700 

307 

48714 

48728 

48742 

48756 

48770 

48785 

48799 

48813 

48827 

48841 

308 

48855 

48869 

48883 

48897 

48911 

48926 

48940 

48954 

48968 

48982 

309 

48996 

49010 

49024 

49038 

49052 

49066 

49080 

49094 

49108 

49122 

310 

49136 

49150 

49164 

49178 

49192 

49206 

49220 

49234 

49248 

49262 

311 

49276 

49290 

49304 

49318 

49332 

49346 

49360 

49374 

49388 

49402 

312 

49415 

49429 

49443 

49457 

49471 

49485 

49499 

49513 

49527 

49541 

313 

49554 

49568 

49582 

49596 

49610 

49624 

49638 

49651 

49665 

49679- 

314 

49693 

49707 

49721 

49734 

49748 

49762 

49776 

49790 

49803 

49817 

315 

49831 

49845 

49859 

49872 

49886 

49900 

49914 

49927 

49941 

49955 

316 

49969 

49982 

49996 

50010 

50024 

50037 

50051 

50065 

50079 

50092 

317 

50106 

50120 

50133 

50147 

50161 

50174 

50188 

50202 

50215 

50229 

318 

50243 

50256 

50270 

50284 

50297 

50311 

50325 

50338 

50352 

50365 

319 

50379 

50393 

50406 

50420 

50433 

50447 

50461 

50474 

50488 

50501 

320 

50515 

50529 

50542 

50556 

50569 

50583 

50596 

50610 

50623 

50637 

321 

50651 

50664 

50678 

50691 

50705 

50718 

50732 

50745 

50759 

50772 

322 

50786 

50709 

50813 

50826 

50840 

50853 

50866 

50880 

50893 

50907 

323 

50920 

50934 

50947 

50961 

50974 

50987 

51001 

51014 

51028 

51041 

324 

51055 

51068 

51081 

51095 

51108 

51121 

51135 

51148 

51162 

51175 

325 

51188 

51202 

51215 

51228 

51242 

51255 

51268 

51282 

51295 

51308 

326 

51322 

51335 

51348 

51362 

51375 

51388 

51402 

51415 

51428 

51441 

327 

51455 

51468 

51481 

51495 

51508 

51521 

51534 

51548 

51561 

51574 

328 

51587 

51601 

51614 

51627 

51640 

51654 

51667 

51680 

51693 

51706 

329 

51720 

51733 

51746 

51759 

51772 

51786 

51799 

51812 

51825 

51838 

330 

51851 

51865 

51878 

51891 

51904 

51917 

51930 

51943 

51957 

51970 

331 

51983 

51996 

52009 

52022 

52035 

52048 

52061 

52075 

52088 

52101 

332 

52114 

52127 

52140 

52153 

52166 

52179 

52192 

52205 

52218 

52231 

333 

52244 

52257 

52270 

52284 

52297 

52310 

52323 

52336 

52349 

52362 

334 

52375 

52388 

52401 

52414 

52427 

52440 

52453 

52466 

52479 

52492 

335 

52504 

52517 

52530 

52543 

52556 

52569 

52582 

52595 

52608 

52621 

386 

52634 

52647 

52660 

52673 

52686 

52699 

52711 

52724 

52737 

52750 

387 

52763 

52776 

52789 

52802 

52815 

52827 

52840 

52853 

52866 

52879 

338 

52892 

52905 

52917 

52930 

52943 

52956 

52969 

52982 

52994 

53007 

339 

53020 

53033 

53046 

53058 

53071 

53084 

53097 

53110 

53122 

53135 

























































































Logarithms from 1 to 10,000 


97 


No. 

0 

1 

2 

3 

4 

5 

6 

7 

8 

9 

340 

53148 

53161 

53173 

53186 

53199 

53212 

53224 

53237 

53250 

53263 

341 

53275 

53288 

53301 

53314 

53326 

53339 

53352 

53364 

53377 

53390 

342 

53403 

53415 

53428 

53441 

53453 

53466 

53479 

53491 

53504 

53517 

343 

53529 

53542 

53555 

53567 

53580 

53593 

53605 

53618 

53631 

53643 

344 

53656 

5366-° 

53681 

53694 

53706 

53719 

53732 

53744 

53757 

53769 

345 

53782 

53794 

53807 

53820 

53832 

53845 

53857 

53870 

53882 

53895 

346 

53908 

53920 

53933 

53945 

53958 

53970 

53983 

53995 

54008 

54020 

347 

54033 

54045 

54058 

54070 

54083 

54095 

54108 

54120 

54133 

54145 

348 

54158 

54170 

54183 

54195 

54208 

54220 

54233 

54245 

54258 

54270 

349 

54283 

54295 

54307 

54320 

54332 

54345 

54357 

54370 

54382 

54394 

350 

54407 

54419 

54432 

54444 

54456 

54469 

54481 

54494 

54506 

54518 

351 

54531 

54543 

54555 

54568 

54580 

54593 

54605 

54617 

54630 

54642 

352 

54654 

54667 

54679 

54691 

54704 

54716 

54728 

54741 

54753 

54765 

353 

54777 

54790 

54802 

54814 

54827 

54839 

54851 

54864 

54876 

54888 

354 

54900 

54913 

54925 

54937 

54949 

54962 

54974 

54986 

54998 

55011 

355 

55023 

55035 

55047 

55060 

55072 

55084 

55096 

55108 

55121 

55133 

356 

55145 

55157 

55169 

55182 

55194 

55206 

55218 

55230 

55242 

55255 

357 

55267 

55279 

55291 

55303 

55315 

55328 

55340 

55352 

55364 

55376 

358 

55388 

55400 

55413 

55425 

55437 

55449 

55461 

55473 

55485 

55497 

359 

55509 

55522 

55534 

55546 

55558 

55570 

55582 

55594 

55606 

55618 

360 

55630 

55642 

55654 

55666 

55678 

55691 

55703 

55715 

55727 

55739 

361 

55751 

55763 

55775 

55787 

55799 

55811 

55823 

55835 

55847 

55859 

362 

55871 

55883 

55895 

55907 

55919 

55931 

55943 

55955 

55967 

55979 

363 

55991 

56003 

56015 

56027 

56038 

56050 

56062 

56074 

56086 

56098 

364 

56110 

56122 

56134 

56146 

56158 

56170 

56182 

56194 

56205 

56217 

365 

56229 

56241 

56253 

56265 

56277 

56289 

56301 

56312 

56324 

56336 

366 

56348 

56360 

56372 

56384 

56396 

56407 

56419 

56431 

56443 

56455 

367 

56467 

56478 

56490 

56502 

56514 

56526 

56538 

56549 

56561 

56573 

368 

56585 

56597 

56608 

56620 

56632 

56644 

56656 

56667 

56679 

56691 

369 

56703 

56714 

56726 

56738 

56750 

56761 

56773 

56785 

56797 

56808 

370 

56820 

56832 

56844 

56855 

56867 

56879 

56891 

56902 

56914 

56926 

371 

56937 

56949 

56961 

56972 

56984 

56996 

57008 

57019 

57031 

57043 

372 

57054 

57066 

57078 

57089 

57101 

57113 

57124 

57136 

57148 

57159 

373 

57171 

57183 

57194 

57206 

57217 

57229 

57241 

57252 

57264 

57276 

374 

57287 

57299 

57310 

57322 

57334 

57345 

57357 

57368 

57380 

57392 

375 

57403 

57415 

57426 

57438 

57449 

57461 

57473 

57484 

57496 

57507 

376 

57519 

57530 

57542 

57553 

57565 

57576 

57588 

57600 

57611 

57623 

377 

57634 

57646 

57657 

57669 

57680 

57692 

57703 

57715 

57726 

57738 

378 

57749 

57761 

57772 

57784 

57795 

57807 

57818 

57830 

57841 

57852 

379 

57864 

57875 

57887 

57898 

57910 

57921 

57933 

57944 

57955 

57967 

380 

57978 

57990 

58001 

58013 

58024 

58035 

58047 

58058 

58070 

58081 

381 

58092 

58104 

58115 

58127 

58138 

58149 

58161 

58172 

58184 

58195 

382 

58206 

58218 

58229 

58240 

58252 

58263 

58274 

58286 

58297 

58309 

383 

58320 

58331 

58343 

58354 

58365 

58377 

58388 

58399 

58410 

58422 

384 

58433 

58444 

58456 

58467 

58478 

58490 

58501 

58512 

58524 

58535 

385 

58546 

58557 

58569 

58580 

58591 

58602 

58614 

58625 

58636 

58647 

386 

58659 

58670 

58681 

58692 

58704 

58715 

58726 

58737 

58749 

58760 

387 

58771 

58782 

58794 

58805 

58816 

58827 

58838 

58850 

58861 

58872 

388 

58883 

58894 

58906 

58917 

58928 

58939 

58950 

58961 

58973 

58984 

389 

58995 

59006 

59017 

59028 

59040 

59051 

59062 

59073 

59084 

59095 

390 

59106 

59118 

59129 

59140 

59151 

59162 

59173 

59184 

59195 

59207 

391 

59218 

59229 

59240 

59251 

59262 

59273 

59284 

59295 

59306 

59318 

392 

59329 

59340 

59351 

59362 

59373 

59384 

59395 

59406 

59417 

59428 

393 

59439 

59450 

59461 

59472 

59483 

59494 

59506 

59517 

59528 

59539 

394 

59550 

59561 

59572 

59583 

59594 

59605 

59616 

59627 

59638 

59649 

395 

59660 

59@71 

59682 

59693 

59704 

59715 

59726 

59737 

59748 

59759 

396 

59770 

59780 

59791 

59802 

59813 

59824 

59835 

59846 

59857 

59868 

397 

59879 

59890 

59901 

59912 

59923 

59934 

59945 

59956 

59966 

59977 

398 

59988 

59999 

60010 

60021 

60032 

60043 

60054 

60065 

60076 

60086 

399 

60097 

60108 

60119 

60130 

60141 

60152 

60163 

60173 

60184 

60105 


N 





















































































98 Logarithms from 1 to 10,000. 


No. 

0 

1 

2 

3 

4 

5 

6 

7 

8 

9 

400 

60206 

60217 

60228 

60239 

60249 

60260 

60271 

60282 

60293 

60304 

401 

60314 

60325 

60336 

60347 

60358 

60369 

60379 

60390 

60401 

60412 

402 

60423 

60433 

60444 

60455 

60466 

60477 

60487 

60498 

60509 

60520 

403 

60531 

60541 

60552 

60563. 

60574 

60584 

60595 

60606 

60617 

60627 

404 

60638 

60649 

60660 

60670 

60681 

60692 

60703 

60713 

60724 

60735 

405 

60746 

60756 

60767 

60778 

60788 

60799 

60810 

60821 

60831 

60842 

406 

60853 

60863 

60874 

60885 

60895 

60906 

60917 

60927 

60938 

60949 

407 

60959 

60970 

60981 

60991 

61002 

61013 

61023 

61034 

61045 

61055 

408 

61066 

61077 

61087 

61098 

61109 

61119 

61130 

61140 

61151 

61162 

409 

61172 

61183 

61194 

61204 

61215 

61225 

61236 

61247 

61257 

61268 

410 

61278 

61289 

61300 

61310 

61321 

61331 

61342 

61352 

61363 

61374 

411 

61384 

61395 

61405 

61416 

61426 

61437 

61448 

61458 

61469 

61479 

412 

61490 

61500 

61511 

61521 

61532 

61542 

61553 

61563 

61574 

61584 

413 

61595 

61606 

61616 

61627 

61637 

61648 

61658 

61669 

61679 

61690 

414 

61700 

61711 

61721 

61731 

61742 

61752 

61763 

61773 

61784 

61794 

415 

61805 

61815 

61826 

61836 

61847 

61857 

61868 

61878 

61888 

61899 

416 

61909 

61920 

61930 

61941 

61951 

61962 

61972 

61982 

61993 

62003 

417 

62014 

62024 

62034 

62045 

62055 

62066 

62076 

62086 

62097 

62107 

413 

62118 

62128 

62138 

62149 

62159 

62170 

62180 

62190 

62201 

62211 

419 

62221 

62232 

62242 

62252 

62263 

62273 

62284 

62294 

62304 

62315 

420 

62325 

62335 

62346 

62356 

62366 

62377 

62387 

62397 

62408 

62418 

421 

62428 

62439 

62449 

62459 

62469 

62480 

62490 

62500 

62511 

62521 

422 

62531 

62542 

62552 

62562 

62572 

62583 

62593 

62603 

62613 

62624 

423 

62634 

62644 

62655 

62665 

62675 

62685 

62696 

62706 

62716 

62726 

424 

62737 

62747 

62757 

62767 

62778 

62788 

62798 

62808 

62818 

62829 

425 

62839 

62849 

62859 

62870 

62880 

62890 

62900 

62910 

62921 

62931 

426 

62941 

62951 

62961 

62972 

62982 

62992 

63002 

63012 

63022 

63033 

427 

63043 

63053 

63063 

63073 

63083 

63094 

63104 

63114 

63124 

63134 

428 

63144 

63155 

63165 

63175 

63185 

63195 

63205 

63215 

63225 

63236 

429 

63246 

63256 

63266 

63276 

63286 

63296 

63306 

63317 

63327 

63337 

430 

63347 

63357 

63367 

63377 

63387 

63397 

63407 

63417 

63428 

63438 

431 

63448 

63458 

63468 

63478 

63488 

63498 

63508 

63518 

63528 

63538 

432 

63548 

63558 

63568 

63579 

63589 

63599 

63609 

63619 

63629 

63639 

433 

63649 

63659 

63669 

63679 

63689 

63699 

63709 

63719 

63729 

63739 

434 

63749 

63759 

63769 

63779 

63789 

63799 

63809 

63819 

63829 

63839 

435 

63849 

63859 

63869 

63879 

63889 

63899 

63909 

63919 

63929 

63939 

436 

63949 

63959 

63969 

63979 

63988 

63998 

64008 

64018 

64028 

64038 

437 

64048 

64058 

64068 

64078 

64088 

64098 

64108 

64118 

64128 

64137 

438 

64147 

64157 

64167 

64177 

64187 

64197 

64207 

64217 

64227 

64237 

439 

64246 

64256 

64266 

64276 

64286 

64296 

64306 

64316 

64326 

64335 

440 

64345 

64355 

64365 

64375 

64385 

64395 

64404 

64414 

64424 

64434 

441 

64444 

64454 

64464 

64473 

64483 

64493 

64503 

64513 

64523 

64532 

442 

64542 

64552 

64562 

64572 

64582 

64591 

64601 

64611 

64621 

64631 

443 

64640 

64650 

64660 

64670 

64680 

64689 

64699 

64709 

64719 

64729 

444 

64*?38 

64748 

64758 

64768 

64777 

64787 

64797 

64807 

64816 

64826 

445 

64836 

64846 

64856 

64865 

64875 

64885 

64895 

64904 

64914 

64924 

446 

64933 

64943 

64953 

64963 

64972 

64982 

64992 

65002 

65011 

65021 

447 

65031 

65010 

65050 

65060 

65070 

65079 

65089 

65099 

65108 

65118 

448 

65128 

65137 

65147 

65157 

65167 

65176 

65186 

65196 

65205 

65215 

449 

65225 

65234 

65244 

65254 

65263 

65273 

65283 

65292 

65302 

65312 

450 

65321 

65331 

65341 

65350 

65360 

65369 

65379 

65389 

65398 

65408 

451 

65418 

65427 

65437 

65447 

65456 

65466 

65475 

65485 

65495 

65504 

452 

65514 

65523 

65533 

65543 

65552 

65562 

65571 

65581 

65591 

65600 

453 

65610 

65619 

65629 

65639 

65648 

65658 

65667 

65677 

65686 

65696 

454 

65706 

65715 

65725 

65734 

65744 

65753 

65763 

65772 

65782 

65792 

455 

65801 

65811 

65820 

65830 

65839 

65849 

65858 

65868 

65877 

65887 

456 

65896 

65906 

65916 

65925 

65935 

65944 

65954 

65963 

65973 

65982 

457 

65992 

66001 

66011 

66020 

66030 

66039 

66049 

66058 

66068 

66077 

458 

66087 

66096 

66106 

66115 

66124 

66134 

66143 

66153 

66162 

66172 

459 

66181 

66191 

66200 

66210 

66219 

66229 

66238 

66247! 

66257 

66266 I 






















































































Logarithms from 1 to 10,000. 99 


No. 

0 

1 

I 2 

3 

4 

5 

6 

7 

8 

9 

460 

66276 

66285 

66295 

66304 

66314 

66323 

66332 

66342 

66351 

66361 

461 

66370 

66380 

66389 

66398 

66408 

66417 

66427 

66436 

66445 

66455 

462 

66464 

66474 

66483 

66492 

66502 

66511 

66521 

66530 

66539 

66549 

463 

66558 

66567 

66577 

66586 

66596 

66605 

66614 

66624 

66633 

66642 

464 

66652 

66661 

66671 

66680 

66689 

66699 

66708 

66717 

66727 

66736 

465 

66745 

66755 

66764 

66773 

66783 

66792 

66801 

66811 

66820 

66829 

466 

66839 

66848 

66857 

66867 

66876 

66885 

66894 

66904 

66913 

66922 

467 

66932 

66941 

66950 

66960 

66969 

66978 

66987 

66997 

67006 

67015 

408 

67025 

67034 

67043 

67052 

67062 

67071 

67080 

67089 

67099 

67108 

469 

67117 

67127 

67136 

67145 

67154 

67164 

67173 

67182 

67191 

67201 

470 

67210 

67219 

67228 

67237 

67247 

67256 

67265 

67274 

67284 

67293 

471 

67302 

67311 

67321 

67330 

67339 

67348 

67357 

67367 

67376 

67385 

472 

67394 

67403 

67413 

67422 

67431 

‘'67440 

67449 

67459 

67468 

67477 

473 

67486 

67495 

67504 

67514 

67523 

67532 

67541 

67550 

67560 

67569 

474 

67578 

67587 

67596 

67605 

67614 

67624 

67633 

67642 

67651 

67660 

475 

67669 

67679 

67688 

67697 

67706 

67715 

67724 

67733 

67742 

67752 

476 

67761 

67770 

67779 

67788 

67797 

67806 

67815 

67825 

67834 

67843 

477 

67852 

67861 

67870 

67879 

67888 

67897 

67906 

67916 

67925 

67934 

478 

67943 

67952 

67961 

67970 

67979 

67988 

67997 

68006 

68015 

68024 

479 

68034 

68043 

68052 

68061 

68070 

68079 

68088 

68097 

68106 

68115 

480 

68124 

68133 

68142 

68151 

68160 

68169 

68178 

68187 

68196 

68205 

481 

68215 

68224 

68233 

68242 

68251 

68260 

68269 

68278 

68287 

68296 

482 

68305 

68314 

68323 

68332 

68341 

68350 

68359 

68368 

68377 

68386 

483 

68395 

68404 

68413 

68422 

68431 

68440 

68449 

68458 

68467 

68476 

484 

68485 

68494 

68502 

68511 

68520 

68529 

68538 

68547 

68556 

68565 

485 

68574 

68583 

68592 

68601 

68610 

68619 

68628 

68637 

68646 

68655 

486 

68664 

68673 

68681 

68690 

68699 

68708 

68717 

68726 

68735 

68744 

487 

68753 

68762 

68771 

68780 

68789 

68797 

68806 

68815 

68824 

68833 

488 

68842 

68851 

68860 

68869 

68878 

68886 

68895 

68904 

68913 

68922 

489 

68931 

68940 

68949 

68958 

68966 

68975 

68984 

68993 

69002 

69011 

490 

69020 

69028 

69037 

69046 

69055 

69064 

69073 

69082 

69090 

69099 

491 

69108 

69117 

69126 

69135 

69144 

69152 

69161 

69170 

69179 

69188 

492 

69197 

69205 

69214 

69223 

69232 

69241 

69249 

69258 

69267 

69276 

493 

69285 

69294 

69302 

69311 

69320 

69329 

69338 

69346 

69355 

69364 

494 

69373 

69381 

69390 

69399 

69408 

69417 

69425 

69434 

69443 

69452 

495 

69461 

69469 

69478 

69487 

69496 

69504 

69513 

69522 

69531 

69539 

496 

69548 

69557 

69566 

69574 

69583 

69592 

69601 

69609 

69618 

69627 

1497 

69636 

69644 

69653 

69662 

69671 

69679 

69688 

69697 

69705 

69714 

j 498 

69723 

69732 

69740 

69749 

69758 

69767 

69775 

69784 

69793 

69801 

499 

69810 

69819 

69827 

69836 

69845 

69854 

69862 

69871 

69880 

69888 

500 

69897 

69906 

69914 

69923 

69932 

69940 

69949 

69958 

69966 

69975 

501 

69984 

69992 

70001 

70010 

70018 

70027 

70036 

70044 

70053 

70062 

1502 

70070 

70079 

70088 

70096 

70105 

70114 

70122 

70131 

70140 

70148 

503 

70157 

70165 

70174 

70183 

70191 

70200 

70209 

70217 

70226 

70234 

504 

70243 

70252 

70260 

70269 

70278 

70286 

70295 

70303 

70312 

70321 

505 

70329 

70338 

70346 

70355 

70364 

70372 

70381 

70389 

70398 

70406 

506 

70415 

70424 

70432 

70441 

70449 

70453 

70467 

70475 

70484 

70492 

j 507 

70501 

70509 

70518 

70526 

70535 

70544 

70552 

70561 

70569 

70578 

508 

70586 

70595 

70603 

70612 

70621 

70629 

70638 

70646 

70655 

70663 

509 

70672 

70680 

70689 

70697 

70706 

70714 

70723 

70731 

70740 

70749 

510 

70757 

70766 

70774 

70783 

70791 

70800 

70808 

70817 

70825 

70834 

51 1 

70842 

70851 

70859 

70868 

70876 

70885 

70893 

70902 

70910 

70919 

512 

70927 

70935 

70944 

70952 

70961 

70969 

70978 

70986 

70995 

71003 

1513 

71012 

71020 

71029 

71037 

71046 

71054 

71063 

71071 

71079 

71088 

514 

71096 

71105 

71113 

71122 

71130 

71139 

71147 

71155 

71164 

71172 

515 

71181 

71189 

71198 

71206 

71214 

71223 

71231 

71240 

71248 

71257 

516 

71265 

71273 

71282 

71290 

71299 

71307 

71315 

71324 

71332 

71341 

517 

71349 

71357 

71366 

71374 

71383 

71391 

71399 

71408 

71416 

71425 

518 

71433 

71441 

71450 

71458 

71466 

71475 

71483 

71492 

71500 

71508 

519 

71517 

71525 1 

71533 

71542 1 

71550 

71559 

71567 

71575 

71584 

71592 

wammaamoamn 


























































































































100 


Logarithms from 1 to 10,000 


No. 

0 

1 1 2 

3 

4 

5 

6 

7 

8 

9 

520 

71600 

71609 71617 

71625 

71634 

71642 

71650 

71659 

71667 

71675 

521 

71684 

71692 71700 

71709 

71717 

71725 

71734 

71742 

71750 

71759 

522 

71767 

71775 71784 

71792 

71800 

71809 

71817 

71825 

71834 

71842 

523 

71850 

71858 71867 

71875 

71883 

71892 

71900 

71908 

71917 

71925 

524 

71933 

71941 71950 

71958 

71966 

71975 

71983 

71991 

71999 

72008 

525 

72016 

72024 72032 

72041 

72049 

72057 

72066 

72074 

72082 

72090 j 

526 

72099 

72107 72115 

72123 

72132 

72140 

72148 

72156 

72165 

72173 j 

527 

72181 

72189 72198 

72206 

72214 

72222 

72230 

72239 

72247 

72255 1 

I 528 

72263 

72272 72280 

72288 

72296 

72304 

72313 

72321 

72329 

72337 | 

j 529 

72346 

72354 | 72362 

72370 

72378 

72387 

72395 

72403 

72411 

72419 

j 530 

72428 

72436 72444 

72452 

72460 

72469 

72477 

72485 

72493 

72501 

I 531 

72509 

72518 72526 

72534 

72542 

72550 

72558 

72567 

72575 

72583 

I 532 

72591 

72599 72607 

72616 

72624 

72632 

72640 

72648 

72656 

72665 

I 533 

72673 

72681 72689 

72697 

72705 

72713 

72722 

72730 

72738 

72746 

1 534 

72754 

72762 72770 

72779 

72787 

72795 

72803 

72811 

72819 

72827 

I 535 

72835 

72843 72852 

72860 

72868 

72876 

72884 

72892 

72900 

72908 

j 536 

72916 

72925 72933 

72941 

72949 

72957 

72965 

72973 

72981 

72989 

I 537 

72997 

73006 73014 

73022 

73030 

73038 

73046 

73054 

73062 

73070 

I 538 

73078 

73086 73094 

73102 

73111 

73119 

73127 

73135 

73143 

73151 

j 539 

73159 

73167 73175 

73183 

73191 

73199 

73207 

73215 

73223 

73231 

I 540 

73239 

73247 73255 

73263 

73272 

73280 

73288 

73296 

73304 

73312 

| 541 

73320 

73328 73336 

73344 

73352 

73360 

73368 

73376 

73384 

73392 

1 542 

73400 

73408 73416 

73424 

73432 

73440 

73448 

73456 

73464 

73472 

| 543 

73480 

73488 73496 

73504 

73512 

73520 

73528 

73536 

73544 

73552 

I 544 

73560 

73568 73576 

73584 

73592 

73600 

73608 

73616 

73624 

73632 

\ 545 

73640 

73648 73656 

73664 

73672 

73679 

73687 

73695 

73703 

73711 

I 546 

73719 

73727 73735 

73743 

73751 

73759 

73767 

73775 

73783 

73791 

547 

73799 

73807 73815 

73823 

73830 

73838 

73846 

73854 

73862 

73870 

[j 548 

73878 

73886 73894 

73902 

73910 

73918 

73926 

73933 

73941 

73949 

1 549 

73957 

73965 73973 

73981 

73989 

73997 

74005 

74013 

74020 

74028 

II 550 

74036 

74044 74052 

74060 

74068 

74076 

74084 

74092 

74099 

74107 

I 551 

74115 

74123 74131 

74139 

74147 

74155 

74162 

74170 

74178 

74186 

I 552 

74194 

74202 74210 

74218 

74225 

74233 

74241 

74249 

74257 

74265 

| 553 

74273 

74280 74288 

74296 

74304 

74312 

74320 

74327 

74335 

74343 

I 554 

74351 

74359 74367 

74374 

74382 

74390 

74398 

74406 

74414 

74421 

|| 555 

74429 

74437 74445 

74453 

74461 

74468 

74476 

74484 

74492 

74500 

N 556 

74507 

74515 74523 

74531 

74539 

74547 

74554 

74562 

74570 

74578 

11 557 

74586 

74593 74601 

74609 

74617 

74624 

74632 

74640 

74648 

74656 

Ij 558 

74663 

74671 74679 

74687 

74695 

74702 

74710 

74718 

74726 

74733 

I 559 

74741 

74749 74757 

74764 

74772 

74780 

74788 

74796 

74803 

74811 

l| 560 

74819 

74827 74834 

74842 

74850 

74858 

74865 

74873 

74881 

74889 

U 561 

74896 

74904 74912 

74920 

74927 

74935 

74943 

74950 

74958 

74966 

I 562 

74974 

74981 74989 

74997 

75005 

75012 

75020 

75028 

75035 

75043 

II 563 

75051 

75059 75066 

75074 

75082 

75089 

75097 

75105 

75113 

75120 

|| 564 

75128 

"5136 75143 

75151 

75159 

75166 

75174 

75182 

75189 

75197 

| 565 

75205 

75213 75220 

75228 

75236 

75243 

75251 

75259 

75266 

75274 

|| 566 

75282 

75289 75297 

75305 

75312 

75320 

75328 

75335 

75343 

75351 

| 567 

75358 

75366 75374 

75381 

75389 

75397 

75404 

75412 

75420 

75427 

| 568 

75435 

75442 75450 

75458 

75465 

75473 

75481 

75488 

75496 

75504 

1 569 

75511 

75519 75526 

75534 

75542 

75549 

75557 

75565 

75572 

75580 

| 570 

75587 

75595 75603 

75610 

75618 

75626 

75633 

75641 

75648 

75656 

| 571 

75664 

75671 75679 

75686 

75694 

75702 

75709 

75717 

75724 

75732 

| 572 

75740 

75747 75755 

75762 

75770 

75778 

75785 

75793 

75800 

75808 

| 573 

75815 

75823 75831 

75838 

75846 

75853 

75861 

75868 

75876 

75884 

| 574 

75891 

75899 75906 

75914 

75921 

75929 

75937 

75944 

75952 

75959 

| 575 

75967 

75974 | 75982 

75989 

75997 

76005 

76012 

76020 

76027 

76035 

| 576 

76042 

76050 | 76057 

76065 

76072 

76080 

76087 

76095 

76103 

76110 

| 577 

76118 

76125 76133 

76140 

76148 

76155 

76163 

76170 

76178 

76185 

| 578 

76193 

76200 76208 

76215 

76223 

76230 

76238 

76245 

76253 

76260 

I 578 

76268 

76275 1 76283 

76290 

76298 

76305 

76313 

76320 

76328 

76335 















































































































Logarithms from 1 to 10,000. 101 


No. 

0 

1 

2 

3 

4 

5 

6 

7 

8 

9 

580 

76343 

76350 

76358 

76365 

76373 

76380 

76388 

76395 

76403 

76410 

581 

76418 

76425 

76433 

76440 

76448 

76455 

76462 

76470 

76477 

76485 

582 

76492 

76500 

76507 

76515 

76522 

76530 

76537 

76545 

76552 

76559 

583 

76567 

76574 

76582 

76589 

76597 

76604 

76612 

76619 

76626 

76634 

584 

76641 

76649 

76656 

76664 

76671 

76678 

76686 

76693 

76701 

76708 

585 

76716 

76723 

76730 

76738 

76745 

76753 

76760 

76768 

76775 

76782 

586 

76790 

76797 

76805 

76812 

76819 

76827 

76834 

76842 

76849 

76856 

587 

76864 

76871 

76879 

76886 

76893 

76901 

76908 

76916 

76923 

76930 

588 

76938 

76945 

76953 

76960 

76967 

76975 

76982 

76989 

76997 

77004 

589 

77012 

77019 

77026 

77034 

77041 

77048 

77056 

77063 

77070 

77078 

590 

77085 

77093 

77100 

77107 

77115 

77122 

77129 

77137 

77144 

77151 

591 

77159 

77166 

77173 

77181 

77188 

77195 

77203 

77210 

77217 

77225 

592 

77232 

77240 

77247 

77254 

77262 

77269 

77276 

77283 

77291 

77298 

593 

77305 

77313 

77320 

77327 

77335 

77342 

77349 

77357 

77364 

77371 

594 

77379 

77386 

77393 

77401 

77408 

77415 

77422 

77430 

77437 

77444 

595 

77452 

77459 

77466 

77474 

77481 

77488 

77495 

77503 

77510 

77517 

596 

77525 

77532 

77539 

77546 

77554 

77561 

77568 

77576 

77583 

77590 

597 

77597 

77605 

77612 

77619 

77627 

77634 

77641 

77648 

77656 

77663 

598 

77670 

77677 

77685 

77692 

77699 

77706 

77714 

77721 

77728 

77735 

599 

77743 

77750 

77757 

77764 

77772 

77779 

77786 

77793 

77801 

77808 

600 

77815 

77822 

77830 

77837 

77844 

77851 

77859 

77866 

77873 

77880 

601 

77887 

77895 

77902 

77909 

77916 

77924 

77931 

77938 

77945 

77952 

602 

77960 

77967 

77974 

77981 

77988 

77996 

78003 

78010 

78017 

78025 

603 

78032 

78039 

78046 

78053 

78061 

78068 

78075 

78082 

78089 

78097 

604 

78104 

78111 

78118 

78125 

78132 

78140 

78147 

78154 

78161 

78168 

605 

78176 

78183 

78190 

78197 

78204 

78211 

78219 

78226 

78233 

78240 

606 

78247 

78254 

78262 

78269 

78276 

78283 

78290 

78297 

78305 

78312 

607 

78319 

78326 

78333 

78340 

78347 

78355 

78362 

78369 

78376 

78383 

608 

78390 

78398 

78405 

78412 

78419 

78426 

78433 

78440 

78447 

78455 

609 

78462 

78469 

78476 

78483 

78490 

78497 

78504 

78512 

78519 

78526 

610 

78533 

78540 

78547 

78554 

78561 

78569 

78576 

78583 

78590 

78597 

611 

78604 

78611 

78618 

78625 

78633 

78640 

78647 

78654 

78661 

78668 

612 

78675 

78682 

78689 

78696 

78704 

78711 

78718 

78725 

78732 

78739 

613 

78746 

78753 

78760 

78767 

78774 

78781 

78789 

78796 

78803 

78810 

614 

78817 

78824 

78831 

78838 

78845' 

’78852 

78859 

78866 

78873 

78880 

615 

78888 

78895 

78902 

78909 

78916 

78923 

78930 

78937 

78944 

78951 

616 

78958 

78965 

78972 

78979 

78986 

78993 

79000 

79007 

79014 

79021 

617 

79029 

79036 

79043 

79050 

79057 

79064 

79071 

79078 

79085 

79092 

618 

79099 

79106 

79113 

79120 

79127 

79134 

79141 

79148 

79155 

79162 

619 

79169 

79176 

79183 

79190 

79197 

79204 

79211 

79218 

79225 

79232 

620 

79239 

79246 

79253 

79260 

79267 

79274 

79281 

79288 

79295 

79302 

621 

79309 

79316 

79323 

79330 

79337 

79344 

79351 

79358 

79365 

79372 

622 

79379 

79386 

79393 

79400 

79407 

79414 

79421 

79428 

79435 

79442 

623 

79449 

79456 

79463 

79470 

79477 

79484 

79491 

79498 

79505 

79511 

624 

79518 

79525 

79532 

79539 

79546 

79553 

79560 

79567 

79574 

79581 

625 

79588 

79595 

79602 

79609 

79616 

79623 

79630 

79637 

79644 

79650 

626 

79657 

79664 

79671 

79678 

79685 

79692 

79699 

79706 

79713 

79720 

627 

79727 

79734 

79741 

79748 

79754 

79761 

79768 

79775 

79782 

79789 

628 

79796 

79803 

79810 

79817 

79824 

79831 

79837 

79844 

79851 

79858 

629 

79865 

79872 

79879 

79886 

79893 

79900 

79906 

79913 

79920 

79927 

630 

79934 

79941 

79948 

79955 

79962 

79969 

79975 

79982 

79989 

79996 

631 

80003 

80010 

80017 

80024 

80030 

80037 

80044 

80051 

80058 

80065 

632 

80072 

80079 

80085 

80092 

80099 

80106 

80113 

80120 

80127 

80134 

633 

80140 

80147 

80154 

80161 

80168 

80175 

80182 

80188 

80195 

80202 

634 

80209 

80216 

80223 

80229 

80236 

80243 

80250 

80257 

80264 

80271 

635 

80277 

80284 

80291 

80298 

80305 

80312 

80318 

80325 

80332 

80339 

636 

80346 

80353 

80359 

80366 

80373 

80380 

80387 

80393 

80400 

80407 

637 

80414 

80421 

80428 

80434 

80441 

80448 

80455 

80462 

80468 

80475 

638 

80482 

80489 

80496 

80502 

80509 

80516 

80523 

80530 

80536 

80543 

639 

80550 

80557 

80564 

80570 

80577 

80584 

80591 

80598 

80604 

8061 1 



















































































102 Logarithms from 1 to 10,000. 


No. 

0 

1 

2 

3 

4 

5 

6 

17 

7 

8 

9 

640 

80618 

80625 

80632 

80638 

80645 

80652 

80659 

80665 

80672 

80679 

641 

80686 

80693 

80699 

80706 

80713 

80720 

80726 

80733 

80740 

80747 

642 

80754 

80760 

80767 

80774 

80781 

80787 

80794 

80801 

80808 

80814 

643 

80821 

80828 

80835 

80841 

80848 

80855 

80862 

80868 

80875 

80882 

644 

80889 

80895 

80902 

80909 

80916 

80922 

80929 

80936 

80943 

80949 

645 

80956 

80963 

80969 

80976 

80983 

80990 

80996 

81003 

81010 

81017 

646 

81023 

81030 

81037 

81043 

81050 

81057 

81064 

81070 

81077 

81084 

647 

81090 

81097 

81104 

81111 

81117 

81124 

81131 

81137 

81144 

81151 

648 

81158 

81164 

81171 

81178 

81184 

81191 

81198 

81204 

81211 

81218 

649 

81224 

81231 

81238 

81245 

81251 

81258 

81265 

81271 

81278 

81285 

650 

81291 

81298 

81305 

81311 

81318 

81325 

81331 

81338 

81345 

81351 

651 

81358 

81365 

81371 

81378 

81385 

81391 

81398 

81405 

81411 

81418 

652 

81425 

81431 

81433 

81445 

81451 

81458 

81465 

81471 

81478 

81485 

j 653 

81491 

81498 

81505 

81511 

81518 

81525 

81531 

81538 

81544 

81551 

654 

81558 

81564 

81571 

81578 

81584 

81591 

81598 

81604 

81611 

81617 

655 

81624 

81631 

81637 

81644 

81651 

81657 

81664 

81671 

81677 

81684 

1 656 

81690 

81697 

81704 

81710 

81717 

81723 

81730 

81737 

81743 

81750 

657 

81757 

81763 

81770 

81776 

81783 

81790 

81796 

81803 

81809 

81816 

1658 

81823 

81829 

81836 

81842 

81849 

81856 

81862 

81869 

81875 

81882 

J 659 

81889 

81895 

81902 

81908 

81915 

81921 

81928 

81935 

81941 

81948 

j 660 

81954 

81961 

81968 

81974 

81981 

81987 

81994 

82000 

82007 

82014 

[661 

82020 

82027 

82033 

82040 

82046 

82053 

82060 

82066 

82073 

82079 

1662 

82086 

82092 

82099 

82105 

82112 

82119 

82125 

82132 

82138 

82145 

j 663 

82151 

82153 

82164 

82171 

82178 

82184 

82191 

82197 

82204 

82210 

1664 

82217 

82223 

82230 

82236 

82243 

82249 

82256 

82263 

82269 

82276 

! 665 

82282 

82289 

82295 

82302 

82308 

82315 

82321 

82328 

82334 

82341 

| 666 

82347 

82354 

82360 

82367 

82373 

82380 

82387 

82393 

82400 

82406 

1667 

82413 

82419 

82426 

82432 

82439 

82445 

82452 

82458 

82465 

82471 

668 

82478 

82484 

82491 

82497 

82504 

82510 

82517 

82523 

82530 

82536 

j 669 

82543 

82549 

82556 

82562 

82569 

82575 

82582 

82588 

82595 

82601 

670 

82607 

82614 

82620 

82627 

82633 

82640 

82646 

82653 

82659 

82666 

i 671 

82672 

82679 

82685 

82692 

82698 

82705 

82711 

82718 

82724 

82730 

672 

82737 

82743 

82750 

82756 

82763 

82769 

82776 

82782 

82789 

82795 

673 

82802 

82808 

82814 

82821 

82827 

82834 

82840 

82847 

82853 

82860 

674 

82866 

82872 

82879 

82885 

82892 

82898 

82905 

82911 

82918 

82924 

' 675 

82930 

82937 

82943 

82950 

82956 

82963 

82969 

82975 

82982 

82988 

676 

82995 

83001 

83008 

83014 

83020 

83027 

83033 

83040 

83046 

83052 

! 677 

83059 

83065 

83072 

83078 

83085 

83091 

83097 

83104 

83110 

83117 

i678 

83123 

83129 

83136 

83142 

83149 

83155 

83161 

83168 

83174 

83181 

679 

83187 

83193 

83200 

83206 

83213 

83219 

83225 

83232 

83238 

83245 

i 680 

83251 

83257 

83264 

83270 

83276 

83283 

83289 

83296 

83302 

83308 

1681 

83315 

83321 

83327 

83334 

83340 

83347 

83353 

83359 

83366 

83372 

i 682 

83373 

83385 

83391 

83398 

83404 

83410 

83417 

83423 

83429 

83436 

683 

83442 

83448 

83455 

83461 

83467 

83474 

83480 

83487 

83493 

83499 

I 684 

83506 

83512 

83518 

83525 

83531 

83537 

83544 

83550 

83556 

83563 

' 685 

83569 

83575 

83582 

83588 

83594 

83601 

83607 

83613 

83620 

83626 

686 

83632 

83639 

83645 

83651 

83658 

83664 

83670 

83677 

83683 

83689 

687 

83696 

83702 

83708 

83715 

83721 

83727 

83734 

83740 

83746 

83753 

1688 

83759 

83765 

83771 

83778 

83784 

83790 

83797 

83803 

83809 

83816 

1689 

83822 

83828 

83835 

83841 

83847 

83853 

83860 

83866 

83872 

83879 

I 690 

83885 

83391 

83897 

83904 

83910 

83916 

83923 

83929 

83935 

83942 

691 

83948 

83954 

83960 

83967 

83973 

83979 

83985 

83992 

83998 

84004 

692 

81011 

84017 

84023 

84029 

84036 

84042 

84048 

84055 

84061 

84067 

! 693 

84073 

84080 

84086 

84092 

84098 

84105 

84111 

84117 

84123 

84130 

694 

84136 

84142 

84148 

84155 

84161 

84167 

84173 

84180 

84186 

84192 

! 695 

84198 

84205 

84211 

84217 

8-4223 

84230 

84236 

84242 

84248 

84255 

696 

84261 

84267 

84273 

84280 

84286 

84292 

84298 

84305 

84311 

84317- 

697 

84323 

84330 

84336 

84342 

84348 

84354 

84361 

84367 

84373 

84379 

698 

84386 

84392 

84398 

84404 

84410 

84417 

84423 

84429 

84435 

84442 

699 

84448 

84454 

84460 

84466 

84173 

84479 

84485 

84491 

84497 

84504 




















































































Logarithms from 1 to 10,000. 103 


11 i\ o. 

0 

1 

2 

3 

4 

5 

6 

7 

8 

9 1 

1 

[|700 

84510 

84516 

84522 

84528 

84535 

84541 

84547 

84553 

84559 

84566j 

lj701 

84572 

84578 

84584 

84590 

84597 

84603 

84609 

84615 

84621 

84628 

I 702 

84634 

84640 

84646 

84652 

84658 

84665 

84671 

84677 

84683 

84689 

11 703 

84696 

84702 

84708 

84714 

84720 

84726 

84733 

84739 

84745 

84751 

1 704 

84757 

84763 

84770 

84776 

84782 

84788 

84794 

84800 

84807 

84813 

I 705 

84819 

84825 

84831 

84837 

84844 

84850 

84856 

84862 

84868 

84874 

706 

84880 

84887 

84893 

84899 

84905 

84911 

84917 

84924 

84930 

84936 

707 

84942 

84948 

84954 

84960 

84967 

84973 

84979 

84985 

84991 

84997 

708 

85003 

85009 

85016 

85022 

85028 

85034 

85040 

85046 

85052 

85058 

709 

85065 

85071 

85077 

85083 

85089 

85095 

85101 

85107 

85114 

85120 

710 

85126 

85132 

85138 

85144 

85150 

85156 

85163 

85169 

85175 

85181 

1 7,1 

85187 

85193 

85199 

85205 

85211 

85217 

85224 

85230 

85236 

85242 

7 02 

85248 

85254 

85260 

85266 

85272 

85278 

85285 

85291 

85297 

85303 

713 

85309 

85315 

85321 

85327 

85333 

85339 

85345 

85352 

85358 

85364 

714 

85370 

85376 

85382 

85388 

85394 

85400 

85406 

85412 

85418 

85425 

715 

85431 

85437 

85443 

85449 

85455 

85461 

85467 

85473 

85479 

85485 

716 

85491 

85497 

85503 

85509 

85516 

85522 

85528 

85534 

85540 

85546 

717 

85552 

85558 

85564 

85570 

85576 

85582 

85588 

85594 

85600 

85606 

718 

85612 

85618 

85625 

*85631 

85637 

85643 

85649 

85655 

85661 

85667 

719 

85673 

85679 

85685 

85691 

85697 

85703 

85709 

85715 

85721 

85727 

720 

85733 

85739 

85745 

85751 

85757 

85763 

85769 

85775 

85781 

85788 

I 721 

85794 

85800 

85806 

85812 

85818 

85824 

85830 

85836 

85842 

85848 

722 

85854 

85860 

85866 

85872 

85878 

85884 

85890 

85896 

85902 

85908 

723 

85914 

85920 

85926 

85932 

85938 

85944 

85950 

85956 

85962 

85968 

I 724 

85974 

85980 

85986 

85992 

85998 

86004 

86010 

86016 

86022 

86028 

I 725 

86034 

86040 

86046 

86052 

86058 

86064 

86070 

86076 

86082 

86088 

I 726 

86094 

86100 

86106 

86112 

86118 

86124 

86130 

86136 

86141 

86147 

I 727 

86153 

86159 

86165 

86171 

86177 

86183 

86189 

86195 

86201 

86207 

728 

86213 

86219 

86225 

86231 

86237 

86243 

86249 

86255 , 

86261 

86267 

I 729 

86273 

86279 

86285 

86291 

86297 

86303 

86308 

86314 

86320 

86326 

I 730 

86332 

86338 

86344 

86350 

86356 

86362 

86368 

86374 

86380 

86386 

1 731 

86392 

86398 

86404 

86410 

86415 

86421 

86427 

86433 

86439 

86445 

732 

86451 

86457 

86463 

86469 

86475 

86481 

86487 

86493 

86499 

86504 

733 

86510 

86516 

86522 

86528 

86534 

86540 

86546 

86552 

86558 

86564 

I 734 

86570 

86576 

86581 

86587 

86593 

86599 

86605 

86611 

86617 

86623 

| 735 

86629 

86635 

86641 

86646 

86652 

86658 

86664 

86670 

86676 

86682 

736 

86688 

86694 

86700 

86705 

86711 

86717 

86723 

86729 

86735 

86741 

737 

86747 

86753 

86759 

86764 

86770 

86776 

86782 

86788 

86794 

86800 

738 

86806 

86812 

86817 

86823 

86829 

86835 

86841 

86847 

86853 

86859 

739 

86864 

86870 

86876 

86882 

86888 

86894 

86900 

86906 

86911 

86917 

I 740 

86923 

86929 

86935 

86941 

86947 

86953 

86958 

86964 

86970 

86976! 

741 

86982 

86988 

86994 

86999 

87005 

87011 

87017 

87023 

87029 

87035 

742 

87040 

87046 

87052 

87058 

87064 

87070 

87075 

87081 

87087 

87093 

743 

87099 

87105 

87111 

87116 

87122 

87128 

87134 

87140 

87146 

87151 

744 

87157 

87163 

87169 

87175 

87181 

87186 

07192 

87198 

87204 

87210 

745 

87216 

87221 

87227 

87233 

87239 

87245 

87251 

87256 

87262 

872681 

746 

87274 

87280 

87286 

87291 

87297 

87303 

87309 

87315 

87320 

87326 

747 

87332 

87338 

87344 

87349 

87355 

87361 

87367 

87373 

87379 

87384 

748 

87390 

87396 

87402 

87408 

87413 

87419 

87425 

87431 

87437 

87442 

749 

87448 

87454 

87460 

87466 

87471 

87477 

87483 

87489 

87495 

87500 

I 750 

87506 

87512 

87518 

87523 

87529 

87535 

87541 

87547 

87552 

87558 

751 

87564 

87570 

87576 

87581 

87587 

87593 

87599 

87604 

87610 

87616 

752 

87622 

87628 

87633 

87639 

87645 

87651 

87656 

87662 

87668 

87674 

I 753 

87679 

87685 

87691 

87697 

87703 

87708 

87714 

87720 

87726 

87731 

I 754 

87737 

87743 

87749 

87754 

87760 

87760 

87772 

87777 

87783 

87789 

755 

87795 

87800 

87806 

87812 

87818 

87823 

87829 

87835 

87841 

87846 

I 756 

87852 

87858 

87864 

87869 

87875 

87881 

87887 

87892 

87898 

87904 

757 

87910 

87915 

87921 

87927 

87933 

87938 

87944 

87950 

87955 

87961 

I 758 

87967 

87973 

87978 

87984 

87990 

87996 

88001 

88007 

88013 

88018 

759 

88024 

88030 

88036 

88041 

88047 

88053 

88058 

88064 

88070 

88076| 






















































































































104 Logarithms from 1 to 10,000. 


No. 

0 

1 

2 

3 

4 

5 

6 

7 

8 

9 

760 

88081 

88087 

88093 

88098 

88104 

88110 

88116 

88121 

88127 

88133 

761 

88138 

88144 

88150 

88156 

88161 

88167 

88173 

88178 

88184 

88190 

762 

88195 

88201 

88207 

88213 

88218 

88224 

88230 

88235 

88241 

88247 

763 

88252 

88258 

88264 

88270 

88275 

88281 

88287 

88292 

88298 

88304 

764 

88309 

88315 

88321 

88326 

88332 

88338 

88343 

88349 

88355 

88360 

765 

88366 

88372 

88377 

88383 

88389 

88395 

88400 

88406 

88412 

88417 

766 

88423 

88429 

88434 

88440 

88446 

88451 

88457 

88463 

88468 

88474 

767 

88480 

88485 

88491 

88497 

88502 

88508 

88513 

88519 

88525 

88530 

768 

88536 

88542 

88547 

88553 

88559 

88564 

88570 

88576 

88581 

88587 

769 

88593 

88598 

88604 

88610 

88615 

88621 

88627 

88632 

88638 

88643 

770 

88649 

88655 

88660 

88666 

88672 

88677 

88683 

88689 

88694 

88700 

771 

88705 

88711 

88717 

88722 

88728 

88734 

88739 

88745 

88750 

88756 

772 

88762 

88767 

88773 

88779 

88784 

88790 

88795 

88801 

88807 

88812 

773 

88818 

88824 

88829 

88835 

88840 

88846 

88852 

88857 

88863 

88868 

774 

88874 

88880 

88885 

88891 

88897 

88902 

88908 

88913 

88919 

'88925 

775 

88930 

88936 

88941 

88947 

88953 

88958 

88964 

88969 

88975 

88981 

776 

88986 

88992 

88997 

89003 

89009 

89014 

89020 

89025 

89031 

89037 

7 i i 

89042 

89048 

89053 

89059 

89064 

89070 

89076 

89081 

89087 

89092 

778 

89098 

89104' 

89109 

89115 

89120 

89126 

89131 

89137 

89143 

89148 

779 

89154 

89159 

89165 

89170 

89176 

89182 

89187 

89193 

89198 

89204 

780 

89209 

89215 

89221 

89226 

89232 

89237 

89243 

89248 

89254 

89260 

781 

89265 

89271 

89276 

89282 

89287 

89293 

89298 

89304 

89310 

89315 

782 

89321 

89326 

89332 

89337 

89343 

89348 

89354 

89360 

89365 

89371 

783 

89376 

89382 

89387 

89393 

89398 

89404 

89409 

89415 

89421 

89426 

784 

89432 

89437 

89443 

89448 

89454 

89459 

89465 

89470 

89476 

89481 

785 

89487 

89492 

89498 

89504 

89509 

89515 

89520 

89526 

89531 

89537 

786 

89542 

89548 

89553 

89559 

89564 

89570 

89575 

89581 

89586 

89592 

787 

89597 

89603 

89609 

89614 

89620 

89625 

89631 

89636 

89642 

89647 

788 

89653 

89658 

89664 

89669 

89675 

89680 

89686 

89691 

89697 

89702 

789 

89708 

89713 

89719 

89724 

89730 

89735 

89741 

89746 

89752 

89757 

' 790 

89763 

89768 

89774 

89779 

89785 

89790 

89796 

89801 

89807 

89812 

791 

89818 

89823 

89829 

89834 

89840 

89845 

89851 

89856 

89862 

89867 

792 

89873 

89878 

89883 

89889 

89894 

89900 

89905 

89911 

89916 

89922 

793 

89927 

89933 

89938 

89944 

89949 

89955 

89960 

89966 

89971 

89977 

794 

89982 

89988 

89993 

89998 

90004 

90009 

90015 

90020 

90026 

90031 

795 

90037 

90042 

90048 

90053 

90059 

90064 

90069 

90075 

90080 

90086 

796 

90091 

90097 

90102 

90103 

90113 

90119 

90124 

90129 

90135 

90140 

797 

90146 

90151 

90157 

90162 

90168 

90173 

90179 

90184 

90189 

90195 

798 

90200 

90206 

90211 

90217 

90222 

90227 

90233 

90238 

90244 

90249 

799 

90255 

90260 

90266 

90271 

90276 

90282 

90287 

90293 

90298 

90304 

800 

90309 

90314 

90320 

90325 

90331 

90336 

90342 

90347 

90352 

90358 

801 

90363 

90369 

90374 

90380 

90385 

90390 

90396 

90401 

90407 

90412 

802 

90417 

90423 

90428 

90434 

90439 

90445 

90450 

90455 

90461 

90466 

803 

90472 

90477 

90482 

90488 

90493 

90499 

90504 

90509 

90515 

90520 

804 

90526 

90531 

90536 

90542 

90547 

90553 

90558 

90563 

90569 

90574 

805 

90580 

90585 

90590 

90596 

90601 

90607 

90612 

90617 

90623 

90628 

806 

90634 

90639 

90644 

90650 

90655 

90660 

90666 

90671 

90677 

90682 

807 

90687 

90693 

90698 

90703 

90709 

90714 

90720 

90725 

90730 

90736 

808 

90741 

90747 

90752 

90757 

90763 

90768 

90773 

90779 

90784 

90789 

809 

90795 

90800 

90806 

90811 

90816 

90822 

90827 

90832 

90838 

90843 

810 

90849 

90854 

90859 

90865 

90870 

90875 

90881 

90886 

90891 

90897 

811 

90902 

90907 

90913 

90918 

90924 

90929 

90934 

90940 

90945 

90950 

812 

90956 

90961 

90966 

90972 

90977 

90982 

90988 

90993 

90998 

91004 

813 

91009 

91014 

91020 

91025 

91030 

91036 

91041 

91046 

91052 

91057 

814 

91062 

91068 

91073 

91078 

91084 

91089 

91094 

91100 

91105 

91110 

815 

91116 

91121 

91126 

91132 

91137 

91142 

91148 

91153 

91158 

91164 

816 

91169 

91174 

91180 

91185 

91190 

91196 

91201 

91206 

91212 

91217 

817 

91222 

91228 

91233 

91236 

91243 

91249 

91254 

91259 

91265 

91270 

818 

91275 

91281 

91286 

91291 

91297 

91302 

91307 

91312 

91318 

91323 

819 

L ... 

91328 

91334 

91339 

91344 

91350 

91355 

91360 

91365 

91371 

91376 

























































































Logarithms from 1 to 10,000 


105 


. 1 

O 

£ ! 

0 

1 

2 

3 

4 

5 

6 

7 

8 

9 

820 

91381 

91387 

91392 

91397 

91403 

91408 

91413 

91418 

91424 

91429 

821 

91434 

91440 

91445 

91450 

91455 

91461 

91466 

91471 

91477 

91482 

822 

91487 

91492 

91498 

91503 

91508 

91514 

91519 

91524 

91529 

91535 

823 

91540 

91545 

91551 

91556 

91561 

91566 

91572 

91577 

91582 

91587 

824 

91593 

91598 

91603 

91609 

91614 

91619 

91624 

91630 

91635 

91640 

825 

91645 

91651 

91656 

91661 

91666 

91672 

91677 

91682 

91687 

91693 

826 

91698 

91703 

91709 

91714 

91719 

91724 

91730 

91735 

91740 

91745 

827 

91751 

91756 

91761 

91766 

91772 

91777 

91782 

91787 

91793 

91798 

828 

91803 

91808 

91814 

91819 

91824 

91829 

91834 

91840 

91845 

91850 

829 

91855 

91861 

91866 

91871 

91876 

91882 

91887 

91892 

91897 

91903 

830 

91908 

91913 

91918 

91924 

91929 

91934 

91939 

91944 

91950 

91955 

831 

91960 

91965 

91971 

91976 

91981 

91986 

91991 

91997 

92002 

92007 

832 

92012 

92018 

92023 

92028 

92033 

92038 

92044 

92049 

92054 

92059 

833 

92065 

92070 

92075 

92080 

92085 

92091 

92096 

92101 

92106 

92111 

834 

92117 

92122 

92127 

92132 

92137 

92143 

92148 

92153 

92158 

92163 

835 

92169 

92174 

92179 

92184 

92189 

92195 

92200 

92205 

92210 

92215 

836 

92221 

92226 

92231 

92236 

92241 

92247 

92252 

92257 

92262 

92267 

837 

92273 

92278 

92283 

92288 

92293 

92298 

92304 

92309 

92314 

92319 

838 

92324 

92330 

92335 

92340 

92345 

92350 

92355 

92361 

92366 

92371 

839 

92376 

92381 

92387 

92392 

92397 

92402 

92407 

92412 

92418 

92423 

840 

92428 

92433 

92438 

92443 

92449 

92454 

92459 

92464 

92469 

92474 

841 

92480 

92485 

92490 

92495 

92500 

92505 

92511 

92516 

92521 

92526 

842 

92531 

92536 

92542 

92547 

92552 

92557 

92562 

92567 

92572 

92578 

843 

92583 

•92588 

92593 

92598 

92603 

92609 

92614 

92619 

92624 

92629 

844 

92634 

92639 

92645 

92650 

92655 

92660 

92665 

92670 

92675 

92681 

845 

92686 

92691 

92696 

92701 

92706 

92711 

92716 

92722 

92727 

92732 

846 

92737 

92742 

92747 

92752 

92758 

92763 

92768 

92773 

92778 

92783 

847 

92788 

92793 

92799 

92804 

92809 

92814 

92819 

92824 

92829 

92834 

848 

92840 

92845 

92850 

92855 

92860 

92865 

92870 

92875 

92881 

92886 

849 

92891 

92896 

92901 

92906 

92911 

92916 

92921 

92927 

92932 

92937 

850 

92942 

92947 

92952 

92957 

92962 

92967 

92973 

92978 

92983 

92988 

851 

92993 

92998 

93003 

93008 

93013 

93018 

93024 

93029 

93034 

93039 

852 

93044 

93049 

93054 

93059 

93064 

93069 

93075 

93080 

93085 

93090 

853 

93095 

93100 

93105 

93110 

93115 

93120 

93125 

93131 

93136 

93141 

854 

93146 

93151 

93156 

93161 

93166 

93171 

93176 

93181 

93186 

93192 

855 

93197 

93202 

93207 

93212 

93217 

93222 

93227 

93232 

93237 

93242 

856 

93247 

93252 

93258 

93263 

93268 

93273 

4332 78 

93283 

93288 

93293 

857 

93298 

93303 

93308 

93313 

93318 

93323 


93334 

93339 

93344 

858 

93349 

93354 

93359 

93364 

93369 

93374 

933 tfr 

93384 

93389 

93394 

859 

93399 

93404 

93409 

93414 

93420 

93425 

93430 

93435 

93440 

93445 

860 

93450 

93455 

93460 

93465 

93470 

93475 

93480 

93485 

P3490 

93495 

861 

93500 

93505 

93510 

93515 

93520 

93526 

93531 

93536 

93541 

93546 

862 

93551 

93556 

93561 

93566 

93571 

93576 

93581 

93586 

93591 

93596 

863 

93601 

93606 

93611 

93616 

93621 

93626 

93631 

93636 

93641 

93646 

864 

93651 

93656 

93661 

93666 

93671 

93676 

93682 

936S7• 

93692 

93697 

865 

93702 

93707 

93712 

93717 

93722 

93727 

93732 

93737 

93742 

93747 

866 

93752 

93757 

93762 

93767 

93772 

93777 

93782 

93787 

93792 

93797 

867 

93802 

93807 

93812 

93817 

93822 

93827 

93832 

93837 

93842 

93847 

868 

93852 

93857 

93862 

93867 

93872 

93877 

93882 

93887 

93892 

93897 

f 869 

93902 

93907 

93912 

93917 

93922 

93927 

93932 

93937 

93942 

93947 

870 

93952 

93957 

93962 

93967 

93972 

93977 

93982 

93987 

93992 

93997 I 

871 

94002 

94007 

94012 

94017 

94022 

94027 

94032 

94037 

94042 

94047 

872 

94052 

94057 

94062 

94067 

94072 

94077 

94082 

94086 

94091 

94096 

873 

94101 

94106 

94111 

94116 

94121 

94126 

94131 

94136 

94141 

94146 

874 

94151 

94156 

94161 

94166 

94171 

94176 

94181 

94186 

94191 

94196 

875 

94201 

94206 

94211 

94216 

94221 

94226 

94231 i 

94236 

94240 

94245 

876 

94250 

94255 

94260 

94265 

94270 

94275 

94280 

94285 

94290 

94295 

877 

94300 

94305 

94310 

94315 

94320 

94325 

94330 

94335 

94340 

94345 

878 

94349 

94354 

94359 

94364 

94369 

94374 

94379 | 

94384 

S4389 

94294 

879 

94399 1 

94404 

94409 

94414 

94419 

94424 

94429 i 

94433 

94438 

94443j 


o 









































































































106 


Logarithms from 1 to 10,000 


No. 

0 

1 

2 

3 

4 

5 

6 

7 

8 

9 

880 

94448 

94453 

94458 

94463 

94468 

94473 

94478 

94483 

94488 

94493 

881 

94498 

94503 

94507 

94512 

94517 

94522 

94527 

94532 

94537 

94542 

882 

94547 

94552 

94557 

94562 

94567 

94571 

94576 

94581 

94586 

94591 

883 

94596 

94601 

94606 

94611 

94616 

94621 

94626 

94630 

94635 

94640 

884 

94645 

94650 

94655 

94660 

94665 

94670 

94675 

94680 

94685 

94689 

885 

94694 

94699 

94704 

94709 

94714 

94719 

94724 

94729 

94734 

94738 

886 

94743 

94748 

94753 

94758 

94763 

94768 

94773 

94778 

94783 

94787 

887 

94792 

94797 

94802 

94807 

94812 

94817 

94822 

94827 

94332 

94836 

888 

94841 

94846 

94851 

94856 

94861 

94866 

94871 

94876 

94880 

94885 

889 

94890 

94895 

94900 

94905 

94910 

94915 

94919 

94924 

94929 

94934 

890 

94939 

94944 

94949 

94954 

94959 

94963 

94968 

94973 

94978 

94983 

891 

94988 

94993 

94998 

95002 

95007 

95012 

95017 

95022 

95027 

95032 

892 

95036 

95041 

95046 

95051 

95056 

95061 

95066 

95071 

95075 

95080 

893 

95085 

95090 

95095 

95100 

95105 

95109 

95114 

95119 

95124 

95129 

894 

95134 

95139 

95143 

95148 

95153 

95158 

95163 

95168 

95173 

95177 

895 

95182 

95187 

95192 

95197 

95202 

95207 

95211 

95216 

95221 

95226 

896 

95231 

95236 

95240 

95245 

95250 

95255 

95260 

95265 

95270 

95274 

897 

95279 

95284 

95289 

95294 

95299 

95303 

95308 

95313 

95318 

95323 

898 

95328 

95332 

95337 

95342 

95347 

95352 

95357 

95361 

95366 

95371 

899 

95376 

95381 

95386 

95390 

95395 

95400 

95405 

95410 

95415 

95419 

900 

95424 

95429 

95434 

95439 

95444 

95448 

95453 

95458 

95463 

95468 

901 

95472 

95477 

95482 

95487 

95492 

95497 

95501 

95506 

95511 

95516 

902 

95521 

95525 

95530 

95535 

95540 

95545 

95550 

95554 

95559 

95564 

903 

95569 

95574 

95578 

95583 

95588 

95593 

95598 

95602 

95607 

95612 

904 

95617 

95622 

95626 

95631 

95636 

95641 

95646 

95650 

95655 

95660 

905 

95665 

95670 

95674 

95679 

95684 

95689 

95694 

95698 

95703 

95708 

906 

95713 

95718 

95722 

95727 

95732 

95737 

95742 

95746 

95751 

95756 

907 

95761 

95766 

95770 

95775 

95780 

95785 

95789 

95794 

95799 

95804 

908 

95809 

95813 

95818 

95823 

95828 

95832 

95837 

95842 

95847 

95852 

909 

95856 

95861 

95866 

95871 

95875 

95880 

95885 

95390 

95895 

95899 

910 

95904 

95909 

95914 

95918 

95923 

95928 

95933 

95938 

95942 

95947 

911 

95952 

95957 

95961 

95966 

95971 

95976 

95980 

95985 

95990 

95995 

912 

95999 

96004 

96009 

96014 

96019 

96023 

96028 

96033 

96038 

96042 

913 

96047 

96052 

96057 

96061 

96066 

96071 

96076 

96080 

96085 

96090 

914 

96095 

96099 

96104 

96109 

96114 

96118 

96123 

96128 

96133 

96137 

915 

96142 

96147 

96152 

96156 

96161 

96166 

96171 

96175 

96180 

96185 

916 

96190 

96194 

96199 

96204 

96209 

96213 

96218 

96223 

96227 

96232 

917 

96237 

96242 

96246 

96251 

96256 

96261 

96265 

96270 

96275 

96280 

918 

96284 

96289 

96294 

96298 

96303 

96308 

96313 

96317 

96322 

96327 

919 

96332 

96336 

96341 

96346 

96350 

96355 

96360 

96365 

96369 

96374 

920 

96379 

96384 

96388 

96393 

96398 

96402 

96407 

96412 

96417 

96421 

921 

96426 

96431 

96135 

96440 

96445 

96450 

96454 

96459 

96464 

96468 

922 

96473 

96478 

96483 

96487 

96492 

96497 

96501 

96506 

96511 

96515 

923 

96520 

96525 

96530 

96534 

96539 

96544 

96548 

96553 

96558 

96562 

924 

96567 

96572 

96577 

96581 

96586 

96591 

96595 

96600 

96605 

96609 

925 

96614 

96619 

96624 

96628 

96633 

96638 

96642 

96647 

96652 

96656 

926 

96661 

96666 

96670 

96675 

96680 

96685 

96689 

96694 

96699 

96703 

927 

96708 

96713 

90717 

96722 

96727 

96731 

96736 

96741 

96745 

96750 

928 

96755 

96759 

96704 

96769 

96774 

96778 

96783 

96788 

96792 

96797 

929 

96802 

96806 

9681 1 

96816 

96820 

96825 

96830 

96834 

96839 

96844 

930 

96848 

96853 

96858 

96862 

96867 

96872 

96876 

96881 

96886 

96890 

931 

96895 

96900 

96904 

96909 

96914 

96918 

96923 

96928 

96932 

96937 

932 

'96942 

96946 

96951 

96956 

96960 

96965 

96970 

96974 

96979 

96984 

933 

96988 

96993 

96997 

97002 

97007 

97011 

97016 

97021 

97025 

97030 

[934 

97035 

97039 

97044 

97049 

97053 

97058 

97063 

97067 

97072 

97077 

935 

97081 

97086 

97090 

97095 

97100 

97104 

97109 

97114 

97118 

97123 

936 

97128 

97132 

97137 

97142 

97146 

97151 

97155 

97160 

97165 

97169 

937 

97174 

97179 

97183 

97188 

"97192 

97197 

97202 

97206 

97211 

97216 

938 

97220 

97225 

97230 

97234 

97239 

97243 

97248 

97253 

97257 

97262 

939 

97267 

97271 

97276 

97280 

97285 

97290 

97294 

97299 

97304 

97308 















































































































Logarithms from 1 to 10,000 


107 


No. 

0 

1 

9 

o 

kJ 

4 

5 

6 

7 

8 

9 

940 

97313 

97317 

97322 

97327 

97331 

97336 

97340 

97345 

97350 

97354 

941 

97359 

97364 

97368 

97373 

97377 

97382 

97387 

97391 

97396 

97400 

942 

97405 

97410 

97414 

97419 

97424 

97428 

97433 

97437 

97442 

97447 

943 

97451 

97456 

97460 

97465 

97470 

97474 

97479 

97483 

97488 

97493 

944 

97497 

97502 

97506 

97511 

97516 

97520 

97525 

97529 

97534 

97539 

945 

97543 

97548 

97552 

97557 

97562 

97566 

97571 

97575 

97580 

97585 

946 

97589 

97594 

97598 

97603 

97607 

97612 

97617 

97621 

97626 

97630 

947 

97635 

97640 

97644 

97649 

97653 

97658 

97663 

97667 

97672 

97676 

948 

97681 

97685 

97690 

97695 

97699 

97704 

97708 

97713 

97717 

97722 

949 

97727 

97731 

97736 

97740 

97745 

97749 

97754 

97759 

97763 

97768 

950 

97772 

97777 

97782 

97786 

97791 

97795 

97800 

97804 

97809 

97813 

951 

97818 

97823 

97827 

97832 

97836 

97841 

97845 

97850 

97855 

97859 

952 

97864 

97868 

97873 

97877 

97882 

97886 

97891 

97896 

97900 

97905 

953 

97909 

97914 

97918 

97923 

97928 

97932 

97937 

97941 

-97946 

97950 

954 

97955 

97959 

97964 

97968 

97973 

97978 

97982 

97987 

97991 

97996 

955 

98000 

98005 

98009 

98014 

98019 

98023 

98028 

98032 

98037 

98041 

956 

98046 

98050 

98055 

98059 

98064 

98068 

98073 

98078 

98082 

98087 

957 

98091 

98096 

98100 

98105 

98109 

98114 

98118 

98123 

98127 

98132 

958 

98137 

98141 

98146 

98150 

98155 

98159 

98164 

98168 

93173 

98177 

959 

98182 

98186 

98191 

98195 

98200 

98204 

98209 

98214 

98218 

98223 

960 

98227 

98232 

98236 

98241 

98245 

98250 

98254 

98259 

98263 

98268 

961 

98272 

98277 

98281 

98286 

98290 

98295 

98299 

98304 

98308 

98313 

962 

98318 

98322 

98327 

98331 

98336 

98340 

98345 

98349 

98354 

98358 

963 

98363 

98367 

98372 

98376 

98381 

98385 

98390 

98394 

98399 

98403 

964 

98408 

98412 

98417 

98421 

98426 

98430 

98435 

98439 

98444 

98448 

965 

98453 

98457 

98462 

98466 

98471 

98475 

98480 

98484 

98489 

98493 

966 

98498 

98502 

98507 

98511 

98516 

98520 

98525 

98529 

98534 

98538 

1967 

98543 

98547 

98552 

98556 

98561 

98565 

98570 

98574 

98579 

98583 

968 

98588 

98592 

9859Z 

98601 

98605 

98610 

98614 

98619 

98623 

98628 

969 

98632 

98637 

98641 

98646 

98650 

98655 

98659 

98664 

98668 

98673 

970 

98677 

98682 

98686 

98691 

98695 

98700 

98704 

98709 

98713 

98717 

971 

98722 

98726 

98731 

98735 

98740 

98744 

98749 

98753 

98758 

98762 

1 972 

98767 

98771 

98776 

98780 

98784 

98789 

98793 

98798 

98802 

98807 

1973 

98811 

98816 

98820 

98825 

98829 

98834 

98838 

98843 

98847 

98851 

1974 

98856 

98860 

98865 

98869 

98374 

98878 

98883 

98887 

98892 

98896 

1 975 

98900 

98905 

98909 

98914 

98918 

98923 

98927 

98932 

98936 

98941 

! 976 

9SM5 

$8049 

98954 

98958 

98963 

98967 

98972 

98976 

98981 

98985 

1977 

98989 

98994 

98998 

99003 

99007 

99012 

99016 

99021 

99025 

99029 

(978 

99034 

99038 

99043 

99047 

99052 

99056 

99061 

99065 

99069 

99074 

979 

99078 

99083 

99087 

99092 

99096 

99100 

99105 

99109 

99114 

99118 

980 

99123 

99127 

99131 

99136 

99140 

99145 

99149 

99154 

99158 

99162 

981 

99167 

99171 

99176 

99180 

99185 

99189 

99193 

99193 

99202 

99207 

982 

99211 

99216 

99220 

99224 

99229 

99233 

99238 

99242 

99247 

99251 

983 

99255 

99260 

99264 

99269 

99273 

99277 

99282 

99286 

99291 

99295 

1984 

99300 

99304 

99308 

99313 

99317 

99322 

99326 

99330 

99335 

99339 

1985 

99344 

99348 

99352 

99357 

99361 

99366 

99370 

99374 

99379 

99383 

(986 

99388 

99392 

99396 

99401 

99405 

99410 

99414 

99419 

99423 

99427 

| 987 

99432 

99436 

99441 

99445 

99449 

99454 

99458 

99463 

99467 

99471 

{988 

99476 

99480 

99484 

99489 

99493 

99498 

99502 

99506 

99511 

99515 

989 

99520 

99524 

99528 

99533 

99537 

99542 

99546 

99550 

99555 

99559 

990 

99564 

99568 

99572 

99577 

99581 

99585 

99590 

99594 

99599 

99603 

991 

99607 

99612 

99616 

99621 

99625 

99629 

99634 

99638 

99642 

99647 

992 

99651 

99656 

99660 

99664 

99669 

99673 

99677 

99682 

99686 

99691 

993 

99695 

99699 

99704 

99708 

99712 

99717 

99721 

99726 

99730 

99734 

994 

99739 

99743 

99747 

99752 

99756 

99760 

99765 

99769 

99774 

99778 

995 

99782 

99787 

99791 

99795 

99800 

99804 

99808 

99813 

99817 

99822 

996 

99826 

99830 

99835 

99839 

99843 

99848 

99852 

99856 

99861 

99865 

997 

99870 

99874 

99878 

99883 

99887 

99891 

99896 

99900 

99904 

99909 

998 

99913 

99917 

99922 

99926 

99930 

99935 

99939 

99944 

99948 

99952 

! 999 

99957 

99961 

99965 

99970 

99974 

99978 

99983 

1 99987 

99991 

99996 


















































































































108 Artificial Sines, Tang, and Sec. 0 Degree 


M. 

Sine. 

Co-sine. 

| Tangent. 

Co-tang. 

Secant. 

Co-secant 


0 

Inf. Neg. 

10.00000 

Inf. Neg. 

Infinite. 

10.00000 

Infinite. 

60 

1 

6.46373 

10.00000 

6.46373 

13.53627 

10.00000 

13.53627 

59 

2 

76476 

00000 

76476 

23524 

00000 

23524 

58 

3 

94085 

00000 

94085 

05915 

00000 

05915 

57 

4 

7.06579 

00000 

7.06579 

12.93421 

00000 

12-93421 

56 

5 

16270 

00000 

16270 

83730 

00000 

83730 

55 

6 

24188 

00000 

24188 

75812 

00000 

75812 

54 

7 

30882 

00000 

30882 

69118 

00000 

69118 

53 

8 

36682 

00000 

36682 

63318 

00000 

63318 

52 

9 

41797 

00000 

41797 

58203 

00000 

58203 

51 

10 

46373 

00000 

46373 

53627 

00000 

53627 

50 

11 

7.50512 

10.00000 

7.50512 

12.49488 

10.00000 

12.49488 

49 

12 

54291 

00000 

54291 

45709 

00000 

45709 

48 

13 

57767 

00000 

57767 

42233 

00000 

42233 

47 

14 

60985 

00000 

60986 

39014 

00000 

39015 

46 

15 

63982 

00000 

63982 

36018 

00000 

36018 

45 

16 

66784 

00000 

66785 

33215 

00000 

33216 

44 

17 

69417 

9.99999 

69418 

30582 

00001 

30583 

43 

18 

71900 

99999 

71900 

28100 

00001 

28100 

42 i 

19 

74248 

99999 

74248 

25752 

00001 

25752 

41 

20 

76475 

99999 

76476 

23524 

00001 

23525 

40 

21 

7.78594 

9.99999 

7.78595 

12.21405 

10.00001 

12.21406 

39 

22 

80615 

99999 

80615 

19385 

00001 

19385 

38 

23 

82545 

99999 

82546 

17454 

00001 

17455 

37 

24 

84393 

99999 

84394 

15606 

00001 

15607 

36 

25 

86166 

99999 

86167 

13833 

00001 

13834 

35 

26 

87870 

99999 

87871 

12129 

00001 

12130 

34 

27 

89509 

99999 

89510 

10490 

00001 

10491 

33 

28 

91088 

99999 

91089 

08911 

00001 

08912 

32 

29 

92612 

99998 

92613 

07387 

00002 

07388 

31 

30 

94084 

99998 

94086 

05914 

00002 

05916 

30 

31 

7.95508 

9.99998 

7.95510 

12.04490 

10.00002 

12.04492 

29 

32 

96887 

99998 

96889 

03111 

00002 

03113 

28 

33 

98223 

99998 

98225 

01775 

00002 

01777 

27 

34 

99520 

99998 

99522 

00478 

00002 

00480 

26 

35 

8.00779 

99998 

8.00781 

11.99219 

00002 

11.99221 

25 

36 

02002 

99998 

, 02004 

97996 

00002 

97998 

24 

37 

03192 

99997 

03194 

96806 

00003 

' 96808 

23 

38 

04350 

99997 

04353 

95647 

00003 

95650 

22 

39 

05478 

99997 

05481 

94519 

00003 

94522 

21 

40 

06578 

99997 

06581 

93419 

00003 

93422 

20 

41 

8.07650 

9.99997 

8.07653 

11.92347 

10.00003 

11.92350 

19 

42 

08696 

99997 

08700 

91300 

00003 

91304 

18 

43 

09718 

99997 

09722 

90278 

00003 

90282 

17 

44 

10717 

99996 

10720 

89280 

00004 

89283 

16 

45 

11693 

99996 

11696 

88304 

00004 

88307 

15 

46 

12647 

99996 

12651 

87349 

00004 

87353 

14 

47 

13581 

99996 

13585 

86415 

00004 

86419 

13 

48 

14495 

99996 

14500 

85500 

00004 

85505 

12 

49 

15391 

99996 

15395 

84605 

00004 

84609 

11 

50 

16268 

99995 

16273 

83727 

00005 

83732 

10 

51 

8.17128 

9.99995 

8.17133 

11.82867 

10.00005 

11.82872 

9 

52 

17971 

99995 

17976 

82024 

00005 

82029 

8 

53 

18798 

99995 

18804 

81196 

00005 

♦ 81202 

7 

54 

19610 

99995 

19616 

80384 

00005 

80390 

6 

55 

20407 

99994 

20413 

79587 

00006 

79593 

5 

56 

21189 

99994 

21195 

78805 

00006 

78811 

4 

57 

21958 

99994 

21964 

78036 

00006 

78042 

3 

58 

22713 

99994 

22720 

77280 

00006 

77287 

2 

59 

23456 

99994 

23462 

76538 

00006 

76544 

1 

60 

24186 

99993 

24192 

75808 

00007 

75814 

0 

-.- 

Co-sine. 

Sine. 

Co-tang. 

Tangent. 

Co-secant 

Secant. 

M. 


89 Degrees 















































































Artificial Sines, Tang, and Sec. 1 Degree. 109 


M. 

Sine. 

Co-sme. 

Tangent. 

1 Co-tang. 

Secant. 

Co-secant 

1 

0 

8.24186 

9.99993 

8.24192 

11.75808 

10.00007 

11.75814 

— 

60 

, 1 

24903 

99993 

24910 

75090 

00007 

75097 

59 

2 

25609 

99993 

25616 

74384 

00007 

74391 

58 

3 

26304 

99993 

26312 

73688 

00007 

73696 

57 

4 

26988 

99992 

26996 

73004 

00008 

73012 

56 

5 

27661 

99992 

27669 

72331 

00008 

72339 

55 

6 

28324 

99992 

28332 

71668 

00008 

71676 

54 

7 

28977 

99992 

28986 

71014 

00008 

71023 

53 

8 

29621 

99992 

29629 

70371 

00008 

70379 

52 

9 

30255 

99991 

30263 

69737 

00009 

69745 

51 

10 

8.30879 

9.99991 

8.30888 

11.69112 

10.00009 

11.69121 

50 

11 

31495 

99991 

31505 

68495 

00009 

68505 

49 

12 

32103 

99990 

32112 

67888 

00010 

67897 

48 

13 

32702 

99990 

32711 

67289 

00010 

67298 

47 

14 

33292 

99990 

33302 

66698 

00010 

66708 

46 

15 

33875 

99990 

33886 

66114 

" 00010 

66125 

45 

16 

34450 

99989 

34461 

65539 

00011 

65550 

44 

17 

35018 

99989 

35029 

64971 

00011 

64982 

43 

18 

35578 

99989 

35590 

64410 

00011 

64422 

42 

19 

36131 

99989 

36143 

63857 

00011 

63869 

41 

20 

8.36678 

9.99988 

8.36689 

11.63311 

10.00012 

11.63322 

40 

21 

37217 

99988 

37229 

62771 

00012 

62783 

39 

22 

37750 

99988 

37762 

62238 

00012 

62250 

38 

| 23 

38276 

99987 

38289 

61711 

00013 

61724 

37 

24 

38796 

99987 

38809 

61191 

00013 

61204 

36 

25 

39310 

99987 

39323 

60677 

00013 

60690 

35 

26 

39818 

99986 

39832 

60168 

00014 

60182 

34 

27 

40320 

99986 

40334 

59666 

00014 

59680 

33 

! 28 

40816 

99986 

40830 

59170 

00014 

59184 

32 

1 29 

41307 

99985 

41321 

58679 

00015 

58693 

31 

30 

8.41792 

9.99985 

8.41807 

11.58193 

10.00015 

11.58208 

30 

31 

42272 

99985 

42287 

57713 

00015 

57728 

29 

32 

42746 

99984 

42762 

57238 

00016 

57254 

28 

33 

43216 

99984 

43232 

56768 

00016 

56784 

27 

j 34 

43680 

99984 

43696 

56304 

00016 

56320 

26 

35 

44139 

99983 

44156 

55844 

00017 

55861 

25 

36 

44594 

99983 

44611 

55389 

00017 

55406 

24 

37 

45044 

99983 

45061 

54939 

00017 

54956 

23 

38 

45489 

99982 

45507 

54493 

00018 

54511 

22 

39 

45930 

99982 

45948 

54052 

00018 

54070 

21 

40 

8.46366 

9.99982 

8.46385 

11.53615 

10.00018 

11.53634 

20 

41 

46799 

99981 

46817 

53183 

00019 

53201 

19 

42 

47226 

99981 

47245 

52755 

00019 

52774 

18 

43 

47650 

99981 

47669 

52331 

00019 

52350 

17 

44 

48069 

99980 

48089 

51911 

00020 

51931 

16 

45 

48485 

99980 

48505 

51495 

00020 

51515 

15 

46 

48896 

99979 

48917 

51083 

00021 

51104 

14 

47 

49304 

99979 

49325 

50675 

00021 

50696 

13 

48 

49708 

99979 

49729 

50271 

00021 

50292 

12 

49 

50108 

99978 

50130 

49870 

00022 

49892 

11 

50 

8.50504 

9.99978 

8.50527 

11.49473 

10.00022 

11.49496 

10 

51 

50897 

99977 

50920 

49080 

00023 

49103 

9 

52 

51287 

99977 

51310 

48690 

00023 

48713 

8 

53 

51673 

99977 

51696 

48304 

00023 

48327 

7 

54 

5.2055 

99976 

52079 

47921 

00024 

47945 

6 

55 

52434 

99976 

52459 

47541 

00024 

47566 

5 

56 

52810 

99975 

52835 

47165 

00025 

47190 

4 

57 

53183 

99975 

53208 

46792 

00025 

46817 

3 

58 

53552 

99974 

53578 

46422 

00026 

46448 

2 

59 

53919 

99974 

53945 

46055 

00026 

46081 

1 

60 

54282 

99974 

54308 

45692 

00026 

45718 

0 


Co-sine. 

Sine. 

Co-tang. 1 

Tangent. 

Do-secant 

Secant. 

M._ 


88 Degrees 











































































110 Artificial Sines, Tang, and Sec. 2 Degrees. 


M. 

Sine. 

Co-sme. 

Tangent. 

Co-tang. 

Secant. I Co-secant 


0 

8.54282 

9.99974 

8.54308 

11.45692 

10.00026 

11.45718 

60 

1 

54642 

99973 

54669 

45331 

00027 

45358 

59 

2 

54999 

99973 

55027 

44973 

00027 

45001 

58 

3 

55354 

99972 

55382 

44618 

00028 

44646 

57 

4 

55705 

99972 

55734 

44266 

00028 

44295 

56 

5 

56054 

99971 

56083 

43917 

00029 

43946 

55 

6 

56400 

99971 

56429 

43571 

00029 

43600 

54 

7 

56743 

99970 

56773 

43227 

00030 

43257 

53 

8 

57084 

99970 

57114 

42886 

00030 

42916 

52 

9 

57421 

99969 

57452 

42548 

00031 

42579 

51 

10 

8.57757 

9.99969 

8.57788 

11.42212 

10.00031 

11.42243 

50 

11 

58089 

99968 

58121 

41879 

00032 

41911 

49 

12 

58419 

99968 

58451 

41549 

00032 

41581 

48 

13 

58747 

99967 

58779 

41221 

00033 

41253 

47 

14 

59072 

99967 

59105 

40895 

00033 

40928 

46 

15 

59395 

99967 

59428 

40572 

00033 

40605 

45 

16 

59715 

99966 

59749 

40251 

00034 

40285 

44 

17 

60033 

99966 

60068 

39932 

00034 

39967 

43 

18 

60349 

99965 

60384 

39616 

00035 

39651 

42 

19 

60662 

99964 

60698 

39302 

00036 

39338 

41 

20 

8.60973 

9.99964 

8.61009 

11.38991 

10.00036 

11.39027 

40 

21 

61282 

99963 

61319 

38681 

00037 

38718 

39 

22 

61589 

99963 

61626 

38374 

00037 

38411 

38 

23 

61894 

99962 

61931 

38069 

00038 

38106 

37 

24 

62196 

99962 

62234 

37766 

00038 

37804 

36 

25 

62497 

99961 

62535 

37465 

00039 

37503 

35 

26 

62795 

99961 

62834 

37166 

00039 

37205 

34 

27 

63091 

99960 

63131 

36869 

00040 

36909 

33 

28 

63385 

99960 

63426 

36574 

00040 

36615 

32 

29 

63678 

99959 

63718 

36282 

00041 

36322 

« 1 

30 

8.63968 

9.99959 

8.64009 

11.35991 

10.00041 

11.36032 

30 

31 

64256 

99958 

64298 

35702 

00042 

35744 

29 

32 

64543 

99958 

64585 

35415 

00042 

35457 

28 

33 

64827 

99957 

64870 

35130 

00043 

35173 

27 

34 

65110 

99956 

65154 

34846 

00044 

34890 

26 

35 

65391 

99956 

65435 

34565 

00044 

34609 

25 

! 36 

65670 

99955 

65715 

34285 

00045 

34330 

24 

1 37 

65947 

99955 

65993 

34007 

00045 

34053 

23 

38 

66223 

99954 

66269 

33731 

00046 

33777 

22 i 

1 39 

66497 

99954 

66543 

33457 

00046 

33503 

21 

40 

8.66769 

9.99953 

8.66816 

11.33184 

10.00047 

11.33231 

20 

41 

67039 

99952 

67087 

32913 

00048 

32961 

19 

42 

67308 

99952 

67356 

32644 

00048 

32692 

18 

43 

67575 

99951 

67624 

32376 

00049 

32425 

17 

44 

67841 

99951 

67890 

32110 

00049 

32159 

16 

1 45 

68104 

99950 

68154 

31846 

00050 

31896 

15 

46 

68367 

99949 

68417 

31583 

00051 

31633 

14 

47 

68627 

99949 

68678 

31322 

00051 

31373 

13 

48 

68886 

99948 

68938 

31062 

00052 

31114 

12 

49 

69144 

99948 

69196 

30804 

00052 

30856 

11 

50 

8.69400 

9.99947 

8.69453 

11.30547 

10.00053 

11.30600 

10 

51 

69654 

99946 

69708 

30292 

00054 

30346 

9 

52 

69907 

99946 

69962 

30038 

00054 

30093 

8 

53 

70159 

99945 

70214 

29786 

00055 

29841 

7 

54 

70409 

99944 

70465 

29535 

00056 

29591 

6 

55 

70658 

99944 

70714 

29286 

00056 

29342 

5 

56 

70905 

99943 

70962 

29038 

00057 

29095 

4 

57 

71151 

99942 

71208 

28792 

00058 

28849 

3 

58 

71395 

99942 

71453 

28547 

00058 

28605 

2 i 

59 

71638 

99941 

71697 

28303 

00059 

28362 

1 

60 

71880 

99940 

71940 

28060 

00060 

28120 

0 


Co-sine. 

Sine. 

Co-tang. 

Tangent. 

I Co-secant 

Secant. 

, M I 


87 Degrees; 

o 


I 































































































Artificial Sines, Tang, and Sec. 3 Degrees. Ill 


m' 

Sine. 

Co-sine. 

Tangent. 

Co-tang. 

Secant. 

Co-secant 


0 

8.71880 

9.99940 

8.71940 

11.28060 

10.00060 

11.281.0 

60 

l 

72120 

99940 

72181 

27819 

00060 

27880 

59 

2 

72359 

99939 

7.2420 

27580 

00061 

27641 

58 

3 

72597 

99938 

72659 

27341 

00062 

27403 

57 

4 

72834 

99938 

72896 

27104 

00062 

27166 

56 

5 

73069 

99937 

73132 

26868 

00063 

26931 

55 

6 

73303 

99936 

73366 

26634 

00064 

26697 

54 

i 

73535 

99936 

73600 

26400 

00064 

26465 

53 

8 

73767 

99935 

73832 

26168 

00065 

26233 

52 

9 

73997 

99934 

74063 

25937 

00066 

26003 

51 

10 

8.74226 

9.99934 

8.74292 

11.25708 

10.00066 

11.25774 

50 

11 

74454 

99933 

74521 

25479 

00067 

25546 

49 

12 

74680 

99932 

74748 

25252 

00068 

25320 

48 

13 

74906 

99932 

74974 

25026 

00068 

25094 

47 

14 

75130 

99931 

75199 

24801 

00069 

24870 

46 

15 

75353 

99930 

75423 

24577 

00070 

24647 

45 

16 

75575 

99929 

75645 

24355 

00071 

24425 

44 

17 

75795 

99929 

75867 

24133 

00071 

24205 

43 

18 

76015 

99928 

76087 

23913 

00072 

23985 

42 

19 

76234 

99927 

76306 

23694 

00073 

23766 

41 

20 

8.76451 

9.99926 

8.76525 

11.23475 

10.00074 

11.23549 

40 

21 

76667 

99926 

76742 

23258 

00074 

23333 

39 

22 

76883 

99925 

76958 

23042 

00075 

23117 

38 

23 

77097 

99924 

77173 

22827 

00076 

22903 

37 

24 

77310 

99923 

77387 

22613 

00077 

22690 

36 

25 

77522 

99923 

77600 

22400 

00077 

22478 

35 

26 

77733 

99922 

77811 

22189 

00078 

22267 

34 

27 

77943 

99921 

78022 

21978 

00079 

22057 

33 

28 

78152 

99920 

78232 

21768 

00080 

21848 

32 

29 

78360 

99920 

78441 

21559 

00080 

21640 

31 

30 

8.78568 

'9.99919 

8.78649 

11.21351 

10.00081 

11121432 

30 

31 

78774 

99918 

78855 

21145 

00082 

21226 

29 

32 

78979 

99917 

79061 

20939 

00083 

21021 

28 

33 

79183 

99917 

79266 

20734 

00083 

20817 

27 

34 

79386 

99916 

79470 

20530 

00084 

20614 

26 

35 

79588 

99915 

79673 

20327 

00085 

20412 

25 

36 

79789 

99914 

79875 

20125 

00086 

20211 

24 

37 

79990 

99913 

80076 

19924 

00087 

20010 

23 

38 

80189 

99913 

80277 

19723 

00087 

19811 

22 

39 

80388 

99912 

80476 

19524 

00088 

19612 

21 

40 

8.80585 

9.99911 

8.80674 

11.19326 

10.00089 

11.19415 

20 

41 

80782 

99910 

80872 

19128 

00090 

19218 

19 

42 

80978 

99909 

81068 

18932 

00091 

19022 

18 

43 

81173 

99909 

81264 

18736 

00091 

18827 

17 

44 

81367 

99908 

81459 

18541 

00092 

18633 

16 

45 

81560 

99907 

81653 

18347 

00093 

18440 

15 

46 

81752 

99906 

81846 

18154 

00094 

18248 

14 

47 

81944 

99905 

82038 

17962 

00095 

18056 

13 

48 

82134 

99904 

82230 

17770 

00096 

17866 

12 

49 

82324 

99904 

82420 

17580 

00096 

17676 

11 

50 

8.82513 

9.99903 

8.82610 

li.17390 

10.00097 

11.17487 

10 

51 

82701 

99902 

82799 

17201 

00098 

17299 

9 

52 

82888 

99901 

82987 

17013 

00099 

17112 

8 

53 

83075 

99900 

83175 

16825 

00100 

16925 

7 

54 

83261 

99899 

83361 

16639 

00101 

16739 

6 

55 

83446 

99898 

83547 

16453 

00102 

16554 

5 

56 

83630 

99898 

83732 

16268 

00102 

16370 

4 

57 

83813 

99897 

83916 

16084 

00103 

16187 

3 

58 

83996 

99896 

84100 

15900 

00104 

16004 

2 

59 

84177 

99895 

84282 

15718 

00105 

15823 

1 

60 

84358 

99894 

84464 

15536 

00106 

15642 

0 

1 Co-sine. 

Sine. 

Co-tang. 

Tangent. 

Co-secant 

Secant. 

M. 


86 Degrees. 





























































































112 


Artificial Sines, Tang, and Sec. 4 Degrees. 


H. 

Sine. 

Co-sine. 

tangent. 

Co-tang. 

Secant. 

Co-secant 


(J 

8.84358 

9.99894 

8.84464 

11.15536 

10.00106 

11.15642 

60 

1 

84539 

99893 

84646 

15354 

00107 

15461 

59 

2 

84718 

99892 

84826 

15174 

00108 

15282 

58 

3 

84897 

99891 

85006 

14994 

00109 

15103 

57 

4 

85075 

99891 

85185 

14815 

00109 

14925 

56 

5 

85252 

99890 

85363 

14637 

00110 

14748 

55 

6 

85429 

99889 

85540 

14460 

00111 

14571 

54 

7 

85605 

99888 

85717 

14283 

00112 

14395 

53 

8 

85780 

99887 

85893 

14107 

00113 

14220 

52 

9 

85955 

99886 

86069 

13931 

00114 

14045 

51 

10 

8.86128 

9.99885 

8.86243 

11.13757 

10.00115 

11.13872 

50 

11 

86301 

99884 

86417 

13583 

00116 

13699 

49 

12 

86474 

99883 

86591 

13409 

00117 

13526 

48 

13 

86645 

99882 

86763 

13237 

00118 

13355 

47 

14 

86816 

99881 

86935 

13065 

00119 

13184 

46 

15 

86987 

99880 

87106 

12894 

00120 

13013 

45 

16 

87156 

99879 

87277 

12723 

00121 

12844 

44 

17 

87325 

99879 

87447 

12553 

00121 

12675 

43 

18 

87494 

99878 

87616 

12384 

00122 

12506 

42 

19 

87661 

99877 

87785 

12215 

00123 

12339 

41 

20 

8.87829 

9.99876 

8.87953 

11.12047 

10.00124 

11.12171 

40 

21 

87995 

99875 

88120 

11880 

00125 

12005 

39 

22 

88161 

99874 

88287 

11713 

00126 

11839 

38 

23 

88326 

99873 

88453 

11547 

00127 

11674 

37 

24 

88490 

99872 

88618 

11382 

00128 

11510 

36 

25 

88654 

99871 

88783 

11217 

00129 

11346 

35 

26 

88817 

99870 

88948 

11052 

00130 

11183 

34 

27 

88980 

99869 

89111 

10889 

00131 

11020 

33 

28 

89142 

99868 

89274 

10726 

00132 

10858 

32 

29 

89304 

99867 

89437 

10563 

00133 

10696 

31 

30 

8.89464 

9.99866 

8.89598 

11.10402 

10.00134 

11.10536 

30 

31 

89625 

99865 

89760 

10240 

00135 

10375 

29 

32 

89784 

99864 

89920 

10080 

00136 

10216 

28 

33 

89943 

99863 

90080 

09920 

00137 

10057 

27 

34 

90102 

99862 

90240 

09760 

00138 

09898 

26 

35 

90260 

99861 

90399 

09601 

00139 

09740 

25 

36 

90417 

99860 

90557 

09443 

00140 

09583 

24 

37 

90574 

99859 

90715 

09285 

00141 

09426 

23 

38 

90730 

99858 

90872 

09128 

00142 

09270 

22 

39 

90885 

99857 

91029 

08971 

00143 

09115 

21 

40 

8.91040 

9.99856 

8.91185 

11.08815 

10.00144 

11.08960 

20 

41 

91195 

99855 

91340 

08660 

00145 

08805 

19 

42 

91349 

99854 

91495 

08505 

00146 

08651 

18 

43 

91502 

99853 

91650 

08350 

00147 

08498 

17 

44 

91655 

99852 

91803 

08197 

00148 

08345 

16 

45 

91807 

99851 

91957 

08043 

00149 

08193 

15 

46 

91959 

99850 

92110 

07890 

00150 

08041 

14 

47 

92110 

99848 

92262 

07738 

00152 

07890 

13 

48 

92261 

99847 

92414 

07586 

00153 

07739 

12 

49 

92411 

99846 

92565 

07435 

00154 

07589 

11 ■ 

50 

8.92561 

9.99845 

8.92716 

11.07284 

10.00155 

11.07439 

10 

51 

92710 

99844 

92866 

07134 

00156 

07290 

9 

52 

92859 

99843 

93016 

06984 

00157 

07141 

8 

53 

93007 

99842 

93165 

06835 

00158 

06993 

7 

54 

93154 

99841 

93313 

06687 

00159 

06846 

6 

55 

93301 

99840 

93462 

06538 

00160 

06699 

5 

56 

93448 

99839 

93609 

06391 

00161 

06552 

4 

57 

93594 

99838 

93756 

06244 

00162 

06406 

3 

58 

93740 

99837 

93903 

06097 

00163 

06260 

2 

59 

93885 

99836 

94049 

05951 

00164 

06115 

1 

60 

94030 

99834 

94195 

05805 

00166 

05970 

0 


Co-sine. 

Sine. 

Co-tang. 

Tangent. 

Co-secant 

Secant. 

M. 


85 Degrees. 







































































Artificial Sines, Tang, and Sec. 5 Degrees. 113 


M. 

Sine. 

Co-sine. 

Tangent. 1 

Cortang. | 

Secant. 

Co-secant 1 


0 

8.94030 

9.99834 

8.94195 

11.05805 

10.00166 

11.05970 

60 

1 

94174 

99833 

94340 

05660 

00167 

05826 

59 

2 

94317 

99832 

94485 

05515 

00168 

05683 

58 

3 

94461 

99831 

94630 

05370 

00169 

05539 

57 

4 

94603 

99830 

94773 

05227 

00170 

05397 

56 

5 

94746 

99329 

94917 

05083 

00171 

05254 

55 

6 

94887 

99828 

95060 

04940 

00172 

05113 

54 

7 

95029 

99827 

95202 

04798 

00173 

04971 

53 

8 

95170 

99825 

95344 

04656 

00175 

04830 

52 

9 

95310 

99824 

95486 

04514 

00176 

04690 

51 

10 

8.95450 

9.99823 

8.95627 

11.04373 

10.00177 

11.04550 

50 

11 

95589 

99822 

95767 

04233 

00178 

04411 

49 

12 

95728 

99821 

95908 

04092 

00179 

04272 

48 

13 

95867 

99820 

96047 

03953 

00180 

04133 

47 

14 

96005 

99819 

96187 

03813 

00181 

03995 

46 

15 

96143 

99817 

96325 

03675 

00183 

03857 

45 

16 

96280 

99816 

96464 

03536 

00184 

03720 

44 

17 

96417 

99815 

96602 

03398 

00185 

03583 

43 

18 

96553 

99814 

96739 

03261 

00186 

03447 

42 

19 

96689 

99813 

96877 

03123 

00187 

03311 

1 

41 

20 

8.96825 

9.99812 

8.97013 

11.02987 

10.00188 

11.03175 

40 

21 

96960 

99810 

97150 

02850 

00190 

03040 

39 

22 

97095 

99809 

97285 

02715 

00191 

02905 

38 

23 

97229 

99808 

97421 

02579 

00192 

02771 

37 

24 

97363 

- 99807 

97556 

02444 

00193 

02637 

36 

25 

97496 

99806 

97691 

02309 

00194 

02504 

35 

26 

97629 

99804 

97825 

02175 

00196 

02371 

34 

27 

97762 

99803 

97959 

02041 

00197 

02238 

33 

28 

97894 

99802 

98092 

01908 

00198 

02106 

32 

29 

98026 

99801 

98225 

01775 

00199 

01974 

31 

30 

8.98157 

9-99800 

8.98358 

11.01642 

10.00200 

11.01843 

30 

31 

98288 

99798 

98490 

01510 

00202 

01712 

29 

32 

98419 

99797 

98622 

01378 

00203 

01581 

28 

33 

98549 

99796 

98753 

01247 

00204 

01451 

27 

34 

98679 

99795 

98884 

01116 

00205 

01321 

26 

35 

98808 

99793 

99015 

00985 

00207 

01192 

25 

36 

98937 

99792 

99145 

00855 

00208 

01063 

24 

37 

99066 

99791 

99275 

00725 

00209 

00934 

23 

38 

99194 

99790 

99405 

00595 

00210 

00806 

22 

39 

'99322 

99788 

99534 

00466 

00212 

00678 

21 

40 

8.99450 

9.99787 

8.99662 

11.00338 

10.00213 

11.00550 

20 

41 

99577 

99786 

99791 

00209 

00214 

00423 

19 

42 

99704 

99785 

99919 

00081 

00215 

00296 

18 

43 

99830 

99783 

9.00046 

10.99954 

00217 

00170 

17 

44 

99956 

99782 

00174 

99826 

00218 

00044 

16 

45 

9.00082 

99781 

00301 

99699 

00219 

10.99918 

15 

46 

00207 

99780 

00427 

99573 

00220 

99793 

14 

47 

00332 

99778 

00553 

99447 

00222 

99668 

13 

48 

00456 

99777 

00679 

99321 

00223 

99544 

12 

49 

00581 

99776 

00805 

99195 

00224 

99419 

11 

50 

9.00704 

9.99775 

9.00930 

10.99070 

10.00225 

10.99296 

10 

51 

00828 

99773 

01055 

98945 

00227 

99172 

9 

52 

00951 

99772 

01179 

98821 

00228 

99049 

8 

53 

01074 

99771 

01303 

98697 

00229 

98926 

7 

54 

01196 

99769 

01427 

98573 

00231 

98804 

6 

55 

01318 

99768 

01550 

98450 

00232 

98682 

5 

56 

01440 

• 99767 

01673 

98327 

00233 

98560 

4 

57 

01561 

99765 

01796 

98204 

00235 

98439 

3 

58 

01682 

99764 

01918 

98082 

00236 

98318 

2 

59 

01803 

99763 

02040 

97960 

00237 

98197 

1 

60 

01923 

99761 

02162 

97838 

00239 

98077 

0 


Co-sine. 

Sine. 

Co-tang. 

Tangent. 

Co-secant 

Secant. 

M. 


P 84 Degrees. 








































































114 ‘ Artificial Sines, Tang, and Sec. 6 Degrees 


M. 

Sine. 

Co-sine. 

Tangent. 

Co-tang. 

Secant. 

Co-secant 


0 

9.01923 

9.99761 

9.02162 

10.97838 

10.00239 

10.98077 

60 

1 

02043 

99760 

02283 

97717 

00240 

97957 

59 

2 

02163 

99759 

02404 

97596 

00241 

97837 

58 

3 

02283 

99757 

02525 

97475 

00243 

97717 

57 

4 

02402 

99756 

02645 

97355 

00244 

97598 

56 

5 

02520 

99755 

02766 

97234 

00245 

97480 

55 

6 

02639 

99753 

02885 

97115 

00247 

97361 

54 

7 

02757 

99752 

03005 

96995 

00248 

97243 

53 

8 

02874 

99751 

03124 

96876 

00249 

97126 

52 

9 

02992 

99749 

03242 

96758 

00251 

97008 

51 

10 

9.03109 

9.99748 

9.03361 

10.96639 

10.00252 

10.96891 

50 

11 

03226 

99747 

03479 

96521 

00253 

96774 

49 

12 

03342 

99745 

03597 

96403 

00255 

96658 

48 

13 

03458 

99744 

03714 

96286 

00256 

96542 

47 

14 

03574 

99742 

03832 

96168 

00258 

96426 

46 

15 

03690 

99741 

03948 

96052 

00259 

96310 

45 

16 

03805 

99740 

04065 

95935 

00260 

96195 

44 

17 

03920 

99738 

04181 

95819 

00262 

96080 

43 

18 

04034 

99737 

04297 

95703 

00263 

95966 

42 

19 

04149 

99736 

04413 

95587 

00264 

95851 

41 

20 

9.04262 

9.99734 

9.04528 

10.95472 

10.00266 

10.95738 

40 

21 

04376 

99733 

04643 

95357 

00267 

95624 

39 

22 

04490 

99731 

04758 

95242 

00269 

95510 

38 

23 

04603 

• 99730 

04873 

95127 

00270 

95397 

37 

24 

04715 

99728 

04987 

95013 

00272 

95285 

36 

25 

04828 

99727 

05101 

94899 

00273 

95172 

35 

26 

04940 

99726 

05214 

94786 

00274 

95060 

34 

27 

05052 

99724 

05328 

94672 

00276 

94948 

33 

28 

05164 

99723 

05441 

94559 

00277 

94836 

32 

29 

05275 

99721 

05553 

94447 

00279 

94725 

31 

30 

9.05386 

9.99720 

9.05666 

10.94334 

10.00280 

10.94614 

30 

31 

05497 

99718 

05778 

94222 

00282 

94503 

29 

32 

05607 

99717 

05890 

94110 

00283 

94393 

28 

33 

05717 

99716 

06002 

93998 

00284 

94283 

27 

34 

05827 

99714 

06113 

93887 

00286 

94173 

26 

35 

05937 

99713 

06224 

93776 

00287 

94063 

25 

36 

06046 

99711 

06335 

93665 

00289 

93954 

24 

37 

06155 

99710 

06445 

93555 

00290 

93845 

23 

38 

06264 

99708 

06556 

93444 

00292 

9^736 

22 

39 

06372 

99707 

06666 

93334 

00293 

93628 

21 

40 

9.06481 

9.99705 

9.06775 

10.93225 

10.00295 

10.93519 

20 

41 

06589 

99704 

06885 

93115 

00296 

93411 

19 

42 

06696 

99702 

06994 

93006 

00298 

93304 

18 

43 

06804 

99701 

07103 

92897 

00299 

93196 

17 

44 

06911 

99699 

07211 

92789 

00301 

93089 

16 

45 

07018 

99698 

07320 

92680 

00302 

92982 

15 

46 

07124 

99696 

07428 

92572 

00304 

* 92876 

14 

47 

07231 

99695 

07536 

92464 

00305 

92769 

13 

48 

07337 

99693 

07643 

92357 

00307 

92663 

a 

49 

07442 

99692 

07751 

92249 

00308 

92558 

11 

50 

9-07548 

9.99690 

9.07858 

10.92142 

10.00310 

10.92452 

10 

51 

07653 

99689 

07964 

92036 

00311 

92347 

9 

52 

07758 

99687 

08071 

91929 

00313 

92242 

8 

53 

07863 

99686 

08177 

91823 

00314 

92137 

7 

54 

07968 

99684 

08283 

91717 

00316 

92032 

6 

55 

08072 

99683 

08389 

91611 

00317 

91928 

5 

56 

08176 

99681 

08495 

91505 

00319 

91824 

4 

57 

08280 

99680 

08600 

91400 

00320 

91720 

3 

58 

08383 

99678 

08705 

91295 

00322 

91617 

2 

59 

08486 

99677 

08810 

91190 

00323 

91514 

1 

60 

08589 

99675 

08914 

91086 

00325 

91411 

0 


| Co-sine. 

Sine. 

Co-tang. 

Tangent. 

Co-sccant 

Secant. 

M. 


■0* 


83 Degrees 









































































Artificial Sines, Tang, and Sec. 7 Degrees. 115 


1 M. 

Sine. 

Co-sine. 

Tangent. 

1 Co-tang. 

Secant. 

| Co-secant 

-1 

I 0 

9.08589 

9.99675 

9.08914 

10.91086 

10.00325 

10.91411 

60 

I 1 

08692 

99674 

09019 

90981 

00326 

91308 

59 (| 

1 2 

08795 

99672 

09123 

90877 

00328 

91205 

58 || 

1 3 

08897 

99670 

09227 

90773 

00330 

91103 

57 | 

1 4 

08999 

99669 

09330 

90670 

00331 

91001 

56 l| 

1 5 

09101 

99667 

09434 

90566 

00333 

90899 

55 || 

6 

09202 

99666 

09537 

90463 

00334 

90798 

54 

1 7 

09304 

99664 

09640 

90360 

00336 

90696 

53 

1 8 

09405 

99663 

09742 

90258 

00337 

90595 

52 | 

I 9 

09506 

99661 

09845 

90155 

00339 

90494 

51 ; 

I 10 

9.09606 

9.99659 

9.09947 

10.90053 

10.00341 

10.90394 

50 I 

I 11 

09707 

99658 

10049 

89951 

00342 

90293 

49 1 

1 12 

09807 

99656 

10150 

89850 

00344 

90193 

48 

f 13 

09907 

99655 

10252 

89748 

00345 

90093 

47 

1 14 

10006 

99653 

10353 

89647 

00347 

89994 

46 1 

J 15 

10106 

99651 

10454 

89546 

00349 

89894 

45 1 

r i6 

10205 

99650 

10555 

89445 

00350 

89795 

44 

L 17 

10304 

99648 

10656 

89344 

00352 

89696 

43 

L 18 

10402 

99647 

10756 

89244 

00353 

89598 

42 

I 19 

10501 

99645 

10856 

89144 

00355 

89499 

41 

! 20 

9.10599 

9.99643 

9.10956 

10.89044 

10.00357 

10.89401 

40 

i 21 

10697 

99642 

11056 

88944 

00358 

89303 

39 | 

f 22 

10795 

99640 

11155 

88845 

00360 

89205 

38 || 

I 23 

10893 

99638 

11254 

88746 

00362 

89107 

37 it 

I 24 

10990 

99637 

11353 

88647 

00363 

89010 

36 | 

I 25 

11087 

99635 

11452 

88548 

00365 

88913 

35 | 

1 26 

11184 

99633 

11551 

88449 

00367 

88816 

34 1 

1 27 

11281 

99632 

11649 

88351 

00368 

88719 

33 1 

I 28 

11377 

99630 

11747 

88253 

00370 

88623 

32 U 

I 29 

11474 

99629 

11845 

.88155 

00371 

88526 

31 

! 30 

9.11570 

9.99627 

9.11943 

10.88057 

10.00373 

10.88430 

30 1 

1 31 

11666 

99625 

12040 

87960 

00375 

88334 

29 

32 

11761 

99624 

12138 

87862 

00376 

88239 

28 | 

33 

11857 

99622 

12235 

87765 

00378 

881^3 

27 I 

] 34 

11952 

99620 

12332 

87668 

00380 

88048 

26 | 

I 35 

12047 

99618 

12428 

87572 

00382 

87953 

25 || 

1 36 

12142 

99617 

12525 

87475 

00383 

87858 

24 

1 37 

12236 

99615 

12621 

87379 

00385 

87764 

23 1 

1 38 

12331 

99613 

12717 

87283 

00387 

87669 

22 | 

I 39 

f . -• 

12425 

99612 

12813 

87187 

00388 

87575 

21 [ 

r4o 

9.12519 

9.99610 

9.12909 

10.87091 

10.00390 

10.87481 

20 

I 41 

12612 

99608 

13004 

86996 

00392 

87388 

19 

l 42 

12706 

99607 

13099 

86901 

00393 

87294 

18 

I 43 

12799 

99605 

13194 

86806 

00395 

87201 

17 

1 44 

12892 

99603 

13289 

86711 

00397 

87108 

16 I 

1 45 

12985 

99601 

13384 

86616 

00399 

87015 

15 

1 46 

13078 

99600 

13478 

86522 

00400 

86922 

14 ! 

1 47 

13171 

99598 

13573 

86427 

00402 

86829 

13 1 

48 

13263 

99596 

13667 

86333 

00404 

86737 

12 

1 49 

13355 

99595 

13761 

86239 

00405 

86645 

n I 

B 50 

9.13447 

9.99593 

9.13854 

10.86146 

10.00407 

10.86553 

10 

B 51 

13539 

99591 

13948 

86052 

00409 

86461 

9 

S 52 

13630 

99589 

14041 

85959 

00411 

86370 

8 1 

B 53 

13722 

99588 

14134 

85866 

00412 

86278 

7 : 

B 54 

13813 

99586 

14227 

85773 

00414 

86187 

6 

B 55 

13904 

99584 

14320 

85680 

00416 

86096 

5 I 

56 

13994 

99582 

14412 

85588 

00418 

86006 

4 [ 

B 57 

14085 

99581 

14504 

85496 

00419 

85915 

3 ! 

B 58 

14175 

99579 

14597 

85403 

00421 

85825 

2 j 

B 59 

14266 

99577 

14688 

85312 

00423 

85734 

1 1 

1 60 

14356 

99575 

14780 

85220 

00425 

85644 

0 i 

|l 

Co-sine. 

Sine. 

Co-tang. 

Tangent. 

2o-secant 

Secant. 

M. J 


82 Degrees 


































































































I 


116 Artificial Sines, Tang, and Sec. 8 Degrees. 


M. 

Sine. 

Co-sine. I 

Tangent. | 

Co-tang. 

Secant. 

Do-secant. 

1 

0 

9.14356 

9.99575 

9.14780 

10.85220 

10.00425 

10.85644 

60 I 

l 

14445 

99574 

14872 

85128 

00426 

85555 

59 

2 

14535 

99572 

14963 

85037 

00428 

85465 

58 ( 

8 

14624 

99570 

15054 

84946 

00430 

85376 

57 

4 

14714 

99568 

15145 

84855 

00432 

85286 

56 

5 

14803 

99566 

15236 

84764 

00434 

85197 

55 

6 

14891 

99565 

15327 

84673 

00435 

85109 

54 I 

7 

14980 

99563 

15417 

84583 

00437 

85020 

53 1 

8 

15069 

99561 

15508 

84492 

00439 

84931 

52 I 

9 

15157 

99559 

15598 

84402 

00441 

84843 

51 I 

10 

9.15245 

9.99557 

9.15688 

10.84312 

10.00443 

10.84755 

50 j 

11 

15333 

99556 

15777 

84223 

00444 

84667 

49 1 

12 

15421 

99554 

15867 

84133 

00446 

84579 

48 I 

13 

15508 

99552 

15956 

84044 

00448 

84492 

47 j 

14 

15596 

99550 

16046 

83954 

00450 

84404 

46 ] 

15 

15683 

99548 

16135 

83865 

00452 

84317 

45 i 

16 

15770 

99546 

16224 

83776 

00454 

84230 

44 I 

17 

15857 

99545 

16312 

83688 

00455 

84143 

43 I 

18 

15944 

99543 

16401 

83599 

00457 

84056 

42 1 

19 

16030 

99541 

16489 

83511 

00459 

83970 

41 1 

20 

9.16116 

9.99539 

9.16577 

10.83423 

10.00461 

10.83884 

40 I 

21 

16203 

99537 

16665 

83335 

00463 

83797 

39 I 

22 

16289 

99£35 

16753 

83247 

00465 

83711 

38 I 

23 

16374 

99533 

16841 

83159 

00467 

83626 

37 1 

24 

16460 

99532 

16928 

83072 

00468 

83540 

36 j 

25 

16545 

99530 

17016 

82984 

00470 

83455 

35 j 

26 

16631 

99528 

17103 

82897 

00472 

83369 

34 1 

27 

16716 

99526 

17190 

82810 

00474 

83284 

33 1 

28 

16801 

99524 

17277 

82723 

00476 

83199 

32 

29 

16886 

99522 

17363 

82637 

00478 

83114 

31 1 

30 

9.16970 

9.99520 

9.17450 

10.82550 

10.00480 

10.83030 

30 J 

31 

17055 

99518 

17536 

82464 

00482 

82945 

29 j 

32 

17139 

99517 

17622 

82378 

00483 

82861 

28 | 

1 33 

17223 

99515 

17708 

82292 

00485 

82777 

27 1 

j 34 

17307 

99513 

17794 

82206 

00487 

82693 

26 j 

35 

17391 

99511 

17880 

82120 

00489 

82609 

25 9 

36 

17474 

99509 

17965 

82035 

00491 

82526 

24 1 

37 

17558 

99507 

18051 

81949 

00493 

82442 

23 1 

38 

17641 

99505 

18136 

81864 

00495 

82359 

22 | 

39 

17724 

99503 

18221 

81779 

00497 

82276 

21 1 

40 

9.17807 

9.99501 

9.18306 

10.81694 

10.00499 

10.82193 

20 I 

41 

17890 

99499 

18391 

81609 

00501 

82110 

19 j 

42 

17973 

99497 

18475 

81525 

00503 

82027 

18 I 

43 

18055 

99495 

18560 

81440 

00505 

81945 

17 1 

44 

18137 

99494 

18644 

81356 

00506 

81863 

16 

45 

18220 

99492 

18728 

81272 

00508 

81780 

15 J 

46 

18302 

99490 

18812 

81188 

00510 

81698 

14 

47 

18383 

99488 

18896 

81104 

00512 

81617 

13 I 

48 

18465 

99486 

18979 

81021 

00514 

81535 

12 J 

49 

18547 

99484 

19063 

80937 

00516 

81453 

11 

50T 

9.18628 

9.99482 

9.19146 

10.80854 

10.00518 

10.81372 

10 | 

51 

18709 

99480 

19229 

80771 

00520 

81291 

9 1 

52 

18790 

99478 

19312 

80688 

00522 

81210 

8 J 

53 

18871 

99476 

19395 

80605 

00524 

81129 

7 j 

54 

18952 

99474 

19478 

80522 

00526 

81048 

6 

55 

19033 

99472 

19561 

80439 

00528 

80967 

5 I 

56 

19113 

99470 

19643 

80357 

00530 

80887 

4 I 

57 

19193 

99468 

19725 

80275 

00532 

80807 

3 1 

58 

i 19273 

99466 

19807 

80193 

00534 

80727 

2 1 

59 

19353 

99464 

19889 

80111 

00536 

80647 

1 J 

60 

19433 

99462 

19971 

80029 

00538 

80567 

0 I 


Co-sine. 

Sine. 

Co-tang. 

Tangent. 

Co-secan. 

Secant. 

M. || 


81 I degrees. 





















































































Artificial Sines, Tang, and Sec. 9 Degrees. 117 


M. 

Sine. 

Co-sine. 

Tangent. 

Co-tang. 

Secant. 

Co-secant 


0 

9.19433 

9.99462 

9.19971 

10.80029 

10.00538 

10.80567 

60 

1 

19513 

99460 

20053 

79947 

00540 

80487 

59 

2 

19592 

99458 

20134 

79866 

00542 

80408 

58 

3 

19672 

99456 

20216 

79784 

00544 

80328 

57 

4 

19751 

99454 

20297 

79703 

00546 

80249 

56 

5 

19830 

99452 

20378 

79622 

00548 

80170 

55 

6 

19909 

99450 

20459 

79541 

00550 

80091 

54 

7 

19988 

99448 

20540 

79460 

00552 

80012 

53 

8 

20067 

99446 

20621 

79379 

00554 

79933 

52 

9 

20145 

99444 

20701 

,79299 

00556 

79855 

51 

10 

9.20223 

9.99442 

9.20782 

10.79218 

10.00558 

10.79777 

50 

11 

20302 

99440 

20862 

79138 

00560 

79698 

49 

12 

20380 

99438 

20942 

79058 

00562 

79620 

48 

13 

20458 

99436 

21022 

78978 

00564 

79542 

47 

14 

20535 

99434 

21102 

78898 

00566 

79465 

46 

15 

20613 

99432 

21182 

78818 

00568 

79387 

45 

16 

20691 

99429 

21261 

78739 

00571 

79309 

44 

17 

20768 

99427 

21341 

78659 

00573 

79232 

43 

18 

20845 

99425 

21420 

78580 

00575 

79155 

42 

19 

20922 

99423 

21499 

78501 

00577 

79078 

41 

20 

9.20999 

9.99421 

9.21578 

10.78422 

10.00579 

10.79001 

40 

21 

21076 

99419 

21657 

78343 

00581 

78924 

39 

22 

21153 

99417 

21736 

78264 

00583 

78847 

38 

23 

21229 

99415 

' 21814 

78186 

00585 

78771 

37 

24 

21306 

99413 

21893 

78107 

00587 

78694 

36 

25 

21382 

99411 

21971 

78029 

00589 

78618 

35 

26 

21458 

99409 

22049 

77951 

00591 

78542 

34 

27 

21534 

99407 

22127 

77873 

00593 

78466 

33 

28 

21610 

99404 

22205 

77795 

00596 

78390 

32 

29 

21685 

99402 

22283 

77717 

00598 

78315 

31 

30 

9.21761 

9.99400 

9.22361 

10.77639 

10.00600 

10.78239 

30 

31 

21836 

99398 

22438 

77562 

00602 

78164 

29 

32 

21912 

99396 

22516 

77484 

00604 

78088 

28 

33 

21987 

99394 

22593 

77407 

00606 

78013 

27 

34 

22062 

99392 

22670 

77330 

00608 

77938 

26 

35 

22137 

99390 

22747 

77253 

00610 

77863 

25 

36 

22211 

99388 

22824 

77176 

00612 

77789 

24 

37 

22286 

99385 

22901 

77099 

00615 

77714 

23 

38 

22361 

99383 

22977 

77023 

00617 

77639 

22 

39 

22435 

99381 

23054 

76946 

00619 

77565 

21 

40 

9.22509 

9.99379 

9.23130 

10.76870 

10.00621 

10.77491 

20 

41 

22583 

99377 

23206 

76794 

00623 

77417 

19 

42 

22657 

99375 

23283 

76717 

00625 

77343 

18 

43 

22731 

99372 

23359 

76641 

00628 

77269 

17 

44 

22805 

99370 

23435 

76565 

00630 

77195 

16 

45 

22878 

99368 

23510 

76490 

00632 

77122 

15 

46 

22952 

99366 

23586 

76414 

00634 

77048 

14 

47 

23025 

99364 

23661 

76339 

00636 

76975 

13 

48 

23098 

99362 

23737 

76263 

00638 

76902 

12 

49 

23171 

99359 

23812 

76188 

00641 

76829 

11 

50 

9.23244 

9.99357 

9.23887 

10.76113 

10.00643 

10.76756 

10 

51 

23317 

99355 

23962 

76038 

00645 

76683 

9 

52 

23390 

99353 

24037 

75963 

00647 

76610 

8 

53 

23462 

99351 

24112 

75888 

00649 

76538 

7 

54 

23535 

99348 

24186 

75814 

00652 

76465 

6 

55 

23607 

99346 

24261 

75739 

00654 

76393 

5 

56 

23679 

99344 

24335 

75665 

00656 

76321 

4 

57 

23752 

99342 

24410 

75590 

00658 

76248 

3 

58 

23823 

99340 

24484 

75516 

00660 

76177 

2 

59 

23895 

99337 

24558 

75442 

00663 

76105 

1 

60 

23967 

99335 

24632 

75368 

00665 

76033 

0 


Co-sine. 

Sine. 

Co-lang. 

Tangent. 

Co-sera nt 

Secant. 

M. 


80 Degrees. 











































































118 Artificial Sines, Tang, and Sec. 10 Degrees. 


\ 1 . 

Sine. 

Co-sine. 

Tangent. 

Co-tang. 

Secant. 

Co-secant 


0 

9.23967 

9.99335 

9.24632 

10.75368 

10.00665 

10.76033 

60 

1 

24039 

99333 

24706 

75294 

00667 

75961 

59 

2 

24110 

99331 

24779 

75221 

00669 

75890 

58 

3 

24181 

99328 

24853 

75147 

00672 

75819 

57 

4 

24253 

99326 

24926 

75074 

00674 

75747 

56 

5 

24324 

99324 

25000 

75000 

00676 

75676 

55 

6 

24395 

99322 

25073 

74927 

00678 

75605 

54 

7 

24466 

99319 

25146 

74854 

00681 

75534 

53 

8 

24536 

99317 

25219 

74781 

00683 

75464 

52 

9 

24607 

99315 

25292 

74708 

00685 

75393 

51 

10 

9.24677 

9.99313 

9.25365 

10.74635 

10.00687 

10.75323 

50 

11 

24748 

99310 

25437 

74563 

00690 

75252 

49 

12 

24818 

99308 

25510 

74490 

00692 

75182 

48 

13 

24888 

99306 

25582 

74418 

00694 

75112 

47 

14 

24958 

99304 

25655 

74345 

00696 

75042 

46 

15 

25028 

99301 

25727 

74273 

00699 

74972 

45 

16 

25098 

99299 

25799 

74201 

00701 

74902 

44 

17 

25168 

99297 

25871 

74129 

00703 

74832 

43 

18 

25237 

99294 

25943 

74057 

00706 

74763 

42 

19 

25307 

99292 

26015 

73985 

00708 

74693 

41 

20 

9.25376 

9.99290 

9.26086 

10.73914 

10.00710 

10.74624 

40 

21 

25445 

99288 

26158 

73842 

00712 

74555 

39 

22 

25514 

99285 

26229 

73771 

00715 

74486 

38 

23 

25583 

99283 

26301 

73699 

00717 

74417 

37 

24 

25652 

99281 

26372 

73628 

00719 

74348 

36 

25 

25721 

99278 

26443 

73557 

00722 

74279 

35 

26 

25790 

99276 

26514 

73486 

00724 

74210 

34 

27 

25858 

99274 

26585 

73415 

00726 

74142 

33 

28 

25927 

99271 

26655 

73345 

00729 

74073 

32 

29 

25995 

99269 

26726 

73274 

00731 

74005 

31 

30 

9.26063 

9.99267 

9.26797 

10.73203 

10.00733 

10.73937 

30 

31 

26131 

99264 

26867 

73133 

00736 

73869 

29 

32 

26199 

99262 

26937 

73063 

00738 

73801 

28 

33 

26267 

99260 

27008 

72992 

00740 

73733 

27 

34 

26335 

99257 

27078 

72922 

00743 

73665 

26 

35 

26403 

99255 

27148 

72852 

00745 

73597 

25 

36 

26470 

99252 

27218 

72782 

00748 

73530 

24 

37 

* 26538 

99250 

27288 

72712 

00750 

73462 

23 

38 

26605 

99248 

27357 

72643 

00752 

73395 

22 

39 

26672 

99245 

27427 

72573 

00755 

73328 

21 

40 

9.26739 

9.99243 

9.27496 

10.72504 

10.00757 

10.73261 

20 

41 

26806 

99241 

27566 

72434 

00759 

73194 

19 

42 

26873 

99238 

27635 

72365 

00762 

73127 

18 

43 

26940 

99236 

27704 

72296 

00764 

73060 

17 

44 

27007 

99233 

27773 

72227 

00767 

72993 

16 

45 

27073 

99231 

27842 

72158 

00769 

72927 

15 

46 

27140 

99229 

27911 

72089 

00771 

72860 

14 

47 

27206 

99226 

27980 

72020 

00774 

72794 

13 

48 

27273 

99224 

28049 

71951 

00776 

72727 

12 

49 

27339 

99221 

28117 

71883 

00779 

72661 

11 

50 

9.27405 

9.99219 

9.28186 

10.71814 

10.00781 

10.72595 

10 

51 

27471 

99217 

28254 

71746 

00783 

72529 

9 

52 

27537 

99214 

28323 

71677 

00786 

72463 

8 

53 

27602 

99212 

28391 

71609 

00788 

72398 

7 

54 

27668 

99209 

28459 

71541 

00791 

72332 

6 

55 

27734 

99207 

28527 

71473 

00793 

72266 

5 

56 

27799 

99204 

28595 

71405 

00796 

72201 

4 

57 

27864 

99202 

28662 

71338 

00798 

72136 

3 

58 

, 27930 

99200 

28730 

71270 

00800 

72070 

2 

59 

27995 

99197 

28798 

71202 

00803 

72005 

1 

60 

28060 

99195 

28865 

71135 

00805 

71940 

0 

— 

Co-sine. 

Sine. 

Co-tang. 

Tangent. 

Co-secant 

Secant. 

M. 


79 Degrees, 









































































Artificial Sines, Tang, and Sec. 11 Degrees. 119 


M. 

Sine. 

1 Co-sine. 

1 Tangent. 

| Co-tang. 

Secant. 

Co-secant 


0 

9.28060 

9.99195 

9.28865 

10.71135 

10.00805 

10.71940 

60 

1 

28125 

99192 

28933 

71067 

00808 

71875 

59 

2 

28190 

99190 

29000 

71000 

00810 

71810 

58 

3 

28254 

99187 

29067 

70933 

00813 

71746 

57 

4 

28319 

99185 

29134 

70866 

✓ 00815 

71681 

56 

5 

28384 

99182 

29201 

70799 

00818 

71616 

55 

6 

28448 

99180 

29268 

70732 

00820 

71552 

54 

7 

28512 

99177 

29335 

70665 

00823 

71488 

53 

8 

28577 

99175 

29402 

70598 

00825 

71423 

52 

9 

28641 

99172 

29468 

70532 

00828 

71359 

51 

10 

9.28705 

9.99170 

9.29535 

10.70465 

10.00830 

10.71295 

50 

11 

28769 

99167 

29601 

70399 

00833 

71231 

49 

12 

28833 

99165 

29668 

70332 

00835 

71167 

48 

13 

28896 

99162 

29734 

70266 

00838 

71104 

47 

14 

28960 

99160 

29800 

70200 

00840 

71040 

46 

15 

29024 

99157 

29866 

70134 

00843 

70976 

45 

16 

29087 

99155 

29932 

70068 

00845 

70913 

44 

17 

29150 

99152 

29998 

70002 

00848 

70850 

43 

18 

29214 

99150 

30064 

69936 

00850 

70786 

42 

19 

29277 

99147 

30130 

69870 

00853 

70723 

41 

20 

9.29340 

9.99145 

9.30195 

10.69805 

10.00855 

10.70660 

40 

21 

29403 

99142 

30261 

69739 

00858 

70597 

39 

22 

29466 

99140 

30326 

69674 

00860 

70534 

38 

23 

29529 

99137 

30391 

69609 

00863 

70471 

37 

24 

29591 

99135 

30457 

69543 

00865 

70409 

36 

25 

29654 

99132 

30522 

69478 

00868 

70346 

35 

26 

29716 

99130 

30587 

69413 

00870 

70284 

34 

27 

29779 

99127 

30652 

69348 

00873 

70221 

33 

28 

29841 

99124 

30717 

69283 

00876 

70159 

32 

29 

29903 

99122 

30782 

69218 

00878 

70097 

31 

30 

9.29966 

9.99119 

9.30846 

10.69154 

10.00881 

10.70034 

30 

31 

30028 

99117 

30911 

69089 

00883 

69972 

29 

32 

30090 

99114 

30975 

69025 

00886 

69910 

28 

33 

30151 

99112 

31040 

68960 

00888 

69849 

27 

34 

30213 

99109 

31104 

68896 

00891 

69787 

26 

35 

30275 

99106 

31168 

68832 

00894 

69725 

25 

36 

30336 

99104 

31233 

68767 

00896 

69664 

24 

37 

30398 

99101 

31297 

68703 

00899 

69602 

23 

38 

30459 

99099 

31361 

68639 

00901 

69541 

22 

39 

30521 

99096 

31425 

68575 

00904 

69479 

21 

40 

9.30582 

9.99093 

9.31489 

10.68511 

10.00907 

10.69418 

20 

41 

30643 

99091 

31552 

68448 

00909 

69357 

19 

42 

30704 

99088 

31616 

68384 

00912 

69296 

18 

43 

30765 

99086 

31679 

68321 

00914 

69235 

17 

44 

30826 

99083 

31743 

68257 

00917 

69174 

16 

45 

30887 

99080 

31806 

68194 

00920 

69113 

15 

46 

30947 

99078 

31870 

68130 

00922 

69053 

14 

47 

31008 

99075 

31933 

68067 

00925 

68992 

13 

48 

31068 

99072 

31996 

68004 

00928 

68932 

12 

49 

31129 

99070 

32059 

67941 

00930 

68871 

11 

50 

9.31189 

9.99067 

9.32122 

10.67878 

10.00933 

10.68811 

10 

51 

31250 

99064 

32185 

67815 

00936 

68750 

9 

52 

31310 

99062 

32248 

67752 

00938 

68690 

8 

53 

31370 

99059 

32311 

67689 

00941 

68630 

7 

54 

. 31430 

99056 

32373 

67627 

00944 

68570 

6 

55 

31490 

99054 

32436 

67564 

00946 

68510 

5 

56 

31549 

99051 

32498 

67502 

00949 

68451 

4 

57 

31609 

99048 

. 32561 

67439 

00952 

68391 

3 

58 

31669 

99046 

32623 

67377 

00954 

68331 

2 

59 

31728 

99043 

32685 

67315 

00957 

68272 

1 

60 

31788 

99040 

32747 

67253 

00960 

68212 

0 

= 

Co-sine. 

Sine. 

Co-tang. 1 

Tangent. 

Co-secant | 

Secant. 

AT 


78 Degrees. 







































































120 Artificial Sines, Tang, and Sec. 12 Degrees. 


I VL 1 

Sine. 

Co-sme. 

Tangent. 

Co-tang. 

Secant. 

Co-secant 


0 i 

9.31788 

9.99040 

9.32747 

10.67253 

10.00960 

10.68212 

60 

1 

31847 

99038 

32810 

67190 

00962 

68153 

59 

2 

31907 

99035 

32872 

67128 

00965 

68093 

58 

3 

31966 

99032 

32933 

67067 

00968 

68034 

57 

4 

32025 

99030 

32995 

67005 

00970 

67975 

56 

5 

32084 

99027 

33057 

66943 

00973 

67916 

55 

6 

32143 

99024 

33119 

66881 

00976 

67857 

54 

7 

32202 

99022 

33180 

66820 

00978 

67798 

53 

8 

32261 

99019 

33242 

66758 

00981 

67739 

52 

9 

32319 

99016 

33303 

66697 

00984 

67681 

51 

10 

9.32378 

9.99013 

9.33365 

10.66635 

10.00987 

10.67622 

50 

11 

32437 

99011 

33426 

66574 

00989 

67563 

49 

12 

32495 

99008 

33487 

66513 

00992 

67505 

48 

13 

32553 

99005 

33548 

66452 

00995 

67447 

47 

14 

32612 

99002 

33609 

66391 

00998 

67388 

46 

15 

32670 

99000 

33670 

66330 

01000 

67330 

45 

16 

32728 

98997 

33731 

66269 

01003 

67272 

44 

17 

32786 

98994 

33792 

66208 

01006 

67214 

43 

18 

32844 

98991 

33853 

66147 

01009 

67156 

42 

19 

32902 

98989 

33913 

66087 

01011 

67098 

41 

20 

9.32960 

9.98986 

9.33974 

10.66026 

10.01014 

10.67040 

40 

21 

33018 

98983 

34034 

65966 

01017 

66982 

39 

22 

33075 

98980 

34095 

65905 

01020 

66925 

38 

23 

33133 

98978 

34155 

65845 

01022 

66867 

37 

24 

33190 

98975 

34215 

65785 

01025 

66810 

36 

25 

33248 

98972 

34276 

65724 

01028 

66752 

35 

26 

33305 

98969 

34336 

65664 

01031 

66695 

34 

27 

33362 

98967 

34396 

65604 

01033 

66638 

33 

28 

33420 

98964 

34456 

65544 

01036 

66580 

32 

29 

33477 

98961 

34516 

65484 

01039 

66523 

31 

30 

9.33534 

9.98958 

9.34576 

TO. 65424 

10.01042 

10.66466 

30 

31 

33591 

98955 

34635 

65365 

01045 

66409 

29 

32 

33647 

98953 

34695 

65305 

01047 

66353 

28 

33 

33704 

98950 

34755 

65245 

01050 

66296 

27 

34 

33761 

98947 

34814 

65186 

01053 

66239 

26 

35 

33818 

98944 

34874 

65126 

01056 

66182 

25 

36 

33874 

98941 

34933 

65067 

01059 

66126 

24 

37 

33931 

98938 

34992 

65008 

01062 

66069 

23 

38 

33987 

98936 

35051 

64949 

01064 

66013 

22 

39 

34043 

98933 

35111 

64889 

01067 

65957 

21 

40 

9.34100 

9.98930 

9.35170 

10.64830 

10.01070 

10.65900 

20 

41 

34156 

98927 

35229 

64771 

01073 

65844 

19 

42 

34212 

98924 

35288 

64712 

01076 

65788 

18 

43 

34268 

98921 

35347 

64653 

01079 

65732 

17 

44 

34324 

98919 

35405 

64595 

01081 

65676 

16 

45 

34380 

98916 

35464 

64536 

01084 

65620 

15 

46 

34436 

98913 

35523 

64477 

01087 

65564 

.14 

47 

34491 

98910 

35581 

64419 

01090 

65509 

13 

48 

34547 

98907 

35640 

64360 

01093 

65453 

12 

49 

34602 

98904 

35698 

64302 

01096 

65398 

11 

50 

9.34658 

9.98901 

9.35757 

10.64243 

10.01099 

10.65342 

10 

51 

34713 

98898 

35815 

64185 

01102 

65287 

9 

52 

34769 

98896 

35873 

64127 

01104 

65231 

8 

53 

34824 

98893 

35931 

64069 

01107 

65176 

7 

54 

34879 

98890 

35989 

64011 

OHIO 

65121 

6 

53 

34934 

98887 

36047 

63953 

01113 

65066 

5 

56 

34989 

98884 

36105 

63895 

01116 

65011 

4 

57 

35044 

98881 

36163 

63837 

01119 

64956 

3 

58 

35099 

98878 

36221 

63779 

01122 

64901 

2 

59 

35154 

98875 

36279 

63721 

01125 

64846 

1 

60 

j - 

. 35209 

98872 

36336 

63664 

01128 

64791 

0 


Co-sine. 

Sine. 

Co-tang. 

1 Tangent. 

Co-secant 

Secant. 

M. 


77 Degrees, 











































































Artificial Sines, Tang, and Sec. 13 Degrees. 121 


M. 

Sine. 

Co-sine. 

Tangent. 

Co-tang. 

Secant. 

Co-secant 


0 

9.35209 

9.98872 

9.36336 

10.63664 

10.01128 

10.04791 

60 

1 

35263 

98869 

36394 

63606 

01131 

64737 

59 

,2 

35318 

98867 

36452 

63548 

01133 

64682 

58 

3 

35373 

98864 

36509 

63491 

01136 

64627 

57 

4 

35427 

98861 

36566 

63434 

01139 

64573 

56 

5 

35481 

98858 

36624 

63376 

01142 

64519 

55 

6 

35536 

98855 

36681 

63319 

01145 

64464 

54 

7 

35590 

98852 

36738 

63262 

01148 

64410 

53 

8 

35644 

98849 

36795 

63205 

01151 

64356 

52 

9 

35698 

98846 

36852 

63148 

01154 

64302 

51 

10 

9.35752 

9.98843 

9.36909 

10.63091 

10.01157 

10.64248 

50 

11 

35806 

98840 

36966 

63034 

01160 

64194 

49 

12 

35860 

98837 

37023 

62977 

01163 

64140 

48 

13 

35914 

98834 

37080 

• 62920 

01166 

64086 

47 

14 

35968 

98831 

37137 

62863 

01169 

64032 

46 

15 

36022 

98828 

37193 

62807 

01172 

63978 

45 

16 

36075 

98825 

37250 

62750 

01175 

63925 

44 

17 

36129 

98822 

37306 

62694 

01178 

63871 

43 

18 

36182 

98819 

37363 

62637 

01181 

63818 

42 

19 

36236 

98816 

37419 

62531 

01184 

63764 

41 

20 

9.36289 

9.98813 

9.37476 

10.62524 

10.01187 

10.63711 

40 

21 

36342 

98810 

37532 

62468 

01190 

63658 

39 

22 

36395 

98807 

37588 

62412 

01193 

63605 

38 

23 

36449 

98804 

37644 

62356 

01196 

63551 

37 

24 

36502 

98801 

37700 

62300 

01199 

63498 

36 

25 

36555 

98798 

37756 

62244 

01202 

63445 

35 

26 

36608 

98795 

37812 

62188 

01205 

63392 

34 

27 

36660 

98792 

37868 

62132 

01208 

63340 

33 

28 

36713 

98789 

37924 

62076 

01211 

63287 

32 

29 

36766 

98786 

37980 

62020 

01214 

63234 

31 

30 

9.36819 

9.98783 

9.38035 

10.61965 

10.01217 

10.63181 

30 

31 

36871 

98780 

38091 

61909 

01220 

63129 

29 

32 

36924 

98777 

38147 

61853 

01223 

63076 

28 

33 

36976 

98774 

38202 

61798 

01226 

63024 

27 

34 

37028 

98771 

38257 

61743 

01229 

62972 

26 

35 

37081 

98768 

38313 

61687 

01232 

62919 

25 

36 

37133 

98765 

38368 

61632 

01235 

62867 

24 

37 

37185 

98762 

38423 

61577 

01238 

62815 

23 

38 

37237 

98759 

38479 

61521 

01241 

62763 

22 

39 

37289 

98756 

38534 

61466 

01244 

62711 

21 

40 

9.37341 

9.98753 

9.38589 

10.61411 

10.01247 

10.62659 

20 

41 

37393 

98750 

38644 

61356 

01250 

62607 

19 

42 

37445 

98746 

v 38699 

61301 

01254 

62555 

18 

43 

37497 

98743 

38754 

61246 

01257 

62503 

17 

44 

37549 

98740 

38808 

61192 

01260 

62451 

16 

45 

37600 

98737 

38863 

61137 

01263 

62400 

15 

46 

37652 

98734 

38918 

61082 

01266 

62348 

14 

47 

37703 

98731 

38972 

61028 

01269 

62297 

13 

43 

37755 

98728 

39027 

60973 

01272 

62245 

12 

49 

37806 

98725 

39082 

60918 

01275 

62194 

11 

50 

9.37858 

9.98722 

9.39136 

10.60864 

10.01278 

10.62142 

10 

51 

37909 

98719 

39190 

60310 

01281 

62091 

9 

52 

37960 

98715 

39245 

60755 

01285 

62040 

8 

53 

38011 

98712 

39299 

60701 

01288 

61989 

7 

54 

38062 

98709 

39353 

60647 

01291 

61938 

6 

55 

38113 

98706 

39407 

60593 

01294 

61887 

5 

56 

38164 

98703 

39461 

60539 

01297 

61836 

4 

57 

38215 

98700 

39515 

60485 

01300 

61785 

3 

58 

38266 

98697 

39569 

60431 

01303 

61734 

2 

59 

38317 

98694 

39623 

60377 

01306 

61683 

1 

60 

38368 

98690 

39677 

60323 

01310 

61632 

0 

j Co-sine. 

Sine. 

Co-tang. 

'Tangent. 

Co-secant 

Secant. 

M. 


Q, 76 Degrees. 



















































































122 Artiiicial Sines, Tang, and Sec. 14 Degrees. 


M. 

Sine. 

Co-sine. 

Tangent. 

Co-tang. 

O 

Secant. 

---- 

Co-secant 


0 

9.38368 

9.98690 

9.39677 

10.60323 

10.01310 

10.61632 

60 

1 

38418 

98687 

39731 

60269 

01313 

61582 

59 

2 

38469 

98684 

39785 

60215 

01316 

61531 


3 

38519 

98681 

39838 

60162 

01319 

61481 

57 

4 

38570 

98678 

39892 

60108 

01322 

61430 

56 

5 

38620 

98675 

39945 

60055 

01325 

61380 

55 

6 

38670 

98671 

39999 

60001 

01329 

61330 

54 

7 

38721 

98668 

40052 

59948 

01332 

61279 

53 

8 

38771 

98665 

40106 

59894 

01335 

61229 

52 

9 

38821 

98662 

40159 

59841 

01338 

61179 

51 

10 

9.38871 

9.98659 

9.40212 

10.59788 

10.01341 

10.61129 

50 

11 

38921 

98656 

40266 

59734 

01344 

61079 

49 

12 

38971 

98652 

40319 

59681 

01348 

61029 

48 

13 

39021 

98649 

40372 

59628 

01351 

60979 

47 

14 

39071 

98646 

40425 

59575 

01354 

60929 

46 

15 

39121 

98643 

40478 

59522 

01357 

60879 

45 

16 

39170 

98640 

40531 

59469 

01360 

60830 

44 

17 

39220 

98636 

40584 

59416 

01364 

60780 

43 

18 

39270 

98633 

40636 

59364 

01367 

60730 

42 

19 

39319 

98630 

40689 

59311 

01370 

60681 

41 

20 

9.39369 

9.98627 

9.40742 

10.59258 

10.01373 

10.60631 

40 

21 

39418 

98623 

40795 

59205 

01377 

60582 

39 

22 

39467 

98620 

40847 

59153 

01380 

60533 

38 

23 

39517 

98617 

40900 

59100 

01383 

60483 

37 

24 

39566 

98614 

40952 

59048 

01386 

60434 

36 

25 

39615 

98610 

41005 

58995 

01390 

60385 

35 

26 

39664 

98607 

41057 

58943 

01393 

60336 

34 

27 

39713 

98604 

41109 

58891 

01396 

60287 

33 

28 

39762 

98601 

41161 

58839 

01399 

60238 

32 

29 

39811 

98597 

41214 

58786 

01403 

60189 

31 

30 

9.39860 

9.98594 

9.41266 

10.58734 

10.01406 

10.60140 

30 

31 

39909 

98591 

41318 

58682 

01409 

60091 

29 

32 

39956 

98588 

41370 

58630 

01412 

60042 

28 

33 

40006 

98584 

41422 

58578 

01416 

59994 

27 

34 

40055 

98581 

41474 

58526 

01419 

59945 

26 

35 

40103 

98578 

41526 

58474 

01422 

69897 

25 

36 

40152 

98574 

41578 

58422 

01426 

59848 

24 

37 

40200 

98571 

41629 

58371 

01429 

59800 

23 

38 

40249 

98568 

41681 

58319 

01432 

59751 

22 

39 

40297 

98565 

41733 

58267 

01435 

59703 

21 

40 

9.40346 

9.98561 

9.41784 

10.58216 

10.01439 

10.59654 

20 

41 

40394 

98558 

41836 

58164 

01442 

59606 

19 

42 

40442 

98555 

41887 

58113 

01445 

59558 

18 

43 

40490 

98551 

41939 

58061 

01449 

59510 

17 

44 

40538 

98548 

41990 

58010 

01452 

59462 

16 

45 

40586 

98545 

42041 

57959 

01455 

59414 

15 

46 

40634 

98541 

42093 

57907 

01459 

59366 

14 

47 

40682 

98538 

42144 

57856 

01462 

59318 

13 

48 

40730 

98535 

42195 

57805 

01465 

59270 

12 

49 

40778 

98531 

42246 

57754 

01469 

59222 

11 

50 

9.40825 

9.98528 

9.42297 

10.57703 

10.01472 

10.59175 

10 

51 

40873 

98525 

42348 

57652 

01475 

59127 

9 

52 

40921 

98521 

42399 

57601 

01479 

59079 

8 

53 

40968 

98518 

42450 

57550 

01482 

59032 

7 

54 

41016 

98515 

42501 

57499 

01485 

58984 

6 

55 

41063 

9851! 

42552 

57448 

01489 

58937 

5 

56 

41111 

98508 

42603 

57397 

01492 

58889 

4 

57 

41158 

98505 

42653 

57347 

01495 

58842 

3 

58 

41205 

98501 

42704 

57296 

01499 

58795 

2 

59 

41252 

98498 

42755 

57245 

01502 

58748 

1 

60 

41300 

98494 

42805 

57195 

01506 

58700 

0 


Do-sine. 

Sine. 

Co-tang. 

Tangent. 

Co-secant. 

Secant.. 

M. 


hafa 


75 Degrees 



















































































Artificial Sines, Tang, and Sec. 15 Degrees. 123 


I M. 

Sine. 

Co-sine. 

Tangent. 

Co-tang. 

Secant. 

Co-secant 

-]| 

I 0 

9.41300 

9.98494 

9.42805 

10.57195 

10.01506 

10.58700 

60 

1 

41347 

98491 

42856 

57144 

01509 

58653 

59 

! 2 

41394 

98488 

42906 

57094 

01512 

58606 

58 

1 3 

41441 

98484 

42957 

57043 

01516 

58559 

57 

4 

41488 

98481 

43007 

56993 

01519 

58512 

56 

5 

41535 

98477 

43057 

56943 

01523 

58465 

55 

1 6 

41582 

98474 

43108 

56892 

01526 

58418 

54 

7 

41628 

98471 

43158 

56842 

01529 

58372 

53 p 

8 

41675 

98467 

43208 

56792 

01533 

58325 

52 

1 9 

41722 

98464 

43258 

56742 

01536 

58278 

51 

! 10 

9.41768 

9.98460 

9.43308 

10.56692 

10.01540 

10.58232 

50 

■ ii 

41815 

98457 

43358 

56642 

01543 

58185 

49 

1 12 

41861 

98453 

43408 

56592 

01547 

58139 

48 

J 13 

41908 

98450 

43458 

56542 

01550 

58092 

47 

14 

41954 

98447 

43508 

56492 

01553 

58046 

46 

15 

42001 

98443 

43558 

56442 

01557 

57999 

45 1 

16 

42047 

98440 

43607 

56393 

01560 

57953 

44 

1 17 

42093 

98436 

43657 

56343 

01564 

57907 

43 

I 18 

42140 

98433 

43707 

56293 

01567 

57860 

42 

19 

42186 

98429 

43756 

56244 

01571 

57814 

41 | 

1 20 

9.42232 

9.98426 

9.43806 

10.56194 

10.01574 

10.57768 

40 

1 21 

42278 

98422 

43855 

56145 

01578 

57722 

39 

22 

42324 

98419 

43905 

56095 

01581 

57676 

38 I 

I 23 

42370 

98415 

43954 

56046 

01585 

57630 

37 

1 24 

42416 

98412 

44004 

55996 

01588 

57584 

36 

1 25 

42461 

98409 

44053 

55947 

01591 

57539 

33 

1 26 

42507 

98405 

44102 

55898 

01595 

57493 

34 

1 27 

42553 

98402 

44151 

55849 

01598 

57447 

33 

1 28 

42599 

98398 

44201 

55799 

01602 

57401 

32 

1 29 

42644 

98395 

44250 

55750 

01605 

57356 

31 

4 30 

9.42690 

9.98391 

9.44299 

10.55701 

10.01609 

10.57310 

30 

31 

42735 

98388 

44348 

55652 

01612 

57265 

29 

32 

42781 

98384 

44397 

55603 

01616 

57219 

28 

33 

42826 

98381 

44446 

55554 

01619 

57174 

27 

34 

42872 

98377 

44495 

55505 

01623 

57128 

26 

35 

42917 

98373 

44544 

55456 

01627 

57083 

25 

36 

42962 

98370 

44592 

55408 

01630 

57038 

24 

37 

43008 

98366 

44641 

55359 

01634 

56992 

23 

38 

43053 

98363 

44690 

55310 

01637 

56947 

99 I 

t 

39 

43098 

98359 

44738 

55262 

01641 

56902 

21 

1 40 

9.43143 

9.98356 

9.44787 

10.55213 

10.01644 

10.56857 

20 

41 

43188 

98352 

44836 

55164 

01648 

56812 

19 

i 42 

43233 

98349 

44884 

55116 

01651 

56767 

18 

l\ 43 

43278 

98345 

44933 

55067 

01655 

56722 

17 

I 44 

43323 

98342 

44981 

55019 

01658 

56677 

16 

1 45 

43367 

98338 

45029 

54971 

01662 

56633 

15 

46 

43412 

98334 

45078 

54922 

01666 

56588 

14 

47 

43457 

98331 

45126 

54874 

01669 

56543 

13 

48 

43502 

98327 

45174 

54826 

01673 

56498 

12 

49 

43546 

98324 

45222 

54778 

01676 

56454 

11 I 

U 50 

9.43591 

9.98320 

9.45271 

10.54729 

10.01680 

10.56409 

10 

R 51 

43635 

98317 

45319 

54681 

01683 

56365 

9 

U 52 

43680 

98313 

45367 

54633 

01687 

56320 

8 I 

j 53 

43724 

98309 

45415 

54585 

01691 

56276 

7 

f] 54 

43769 

98306 

45463 

54537 

01694 

56231 

6 

1 55 

43813 

98302 

45511 

54489 

01698 

56187 

5 

j 56 

43857 

98299 

45559 

54441 

01701 

56143 

4 I 

I 57 

43901 

98295 

45606 

54394 

01705 

56099 

3 I 

1 68 

43946 

98291 

45654 

54346 

01709 

56054 

2 I 

59 

43990 

98288 

45702 

54298 

01712 

56010 

1 I 

j 60 

41034 

98284 

45750 

54250 

01716 

55966 

0 I 

|l * 

Co-sine. 

Sine. j 

Co-tang. 

Tangent. 

(Jo-secant 

Secant. | 

1 VI. I 




























































































124 Artificial Sines, Tang, and Sec. 16 Degrees. 


M. 

Sine. 

Co-sine. 

Tangent. 

Co-tang. 

Secant. 

Co-secant 


0 

9.44034 

9.98284 

9.45750 

10.54250 

10.01716 

10.55966 

60 

1 

44078 

98281 

45797 

54203 

01719 

55922 

59 

2 

44122 

98277 

45845 

54155 

' 01723 

55878 

58 

3 

44166 

98273 

45892 

54108 

01727 

55834 

57 

4 

44210 

98270 

45940 

54060 

01730 

55790 

56 

5 

44253 

98266 

45987 

54013 

01734 

55747 

55 

6 

44297 

98262 

46035 

53965 

01738 

55703 

54 

7 

44341 

98259 

46082 

53918 

01741 

55659 

53 

8 

44385 

98255 

46130 

53870 

01745 

55615 

52 

9 

44428 

98251 

46177 

53823 

01749 

55572 

51 

10 

9.44472 

9.98248 

9.46224 

10.53776 

10.01752 

10.55528 

50 

i 11 

44516 

98244 

46271 

53729 

01756 

55484 

49 

12 

44559 

98240 

46319 

53631 

01760 

55441 

48 

13 

44602 

98237 

46366 

53634 

01763 

55398 

47 

14 

44646 

98233 

46413 

53587 

01767 

55354 

46 

15 

44689 

98229 

46460 

53540 

01771 

55311 

45 

16 

44733 

98226 

46507 

53493 

01774 

55267 

44 

17 

44776 

98222 

46554 

53446 

01778 

55224 

43 

18 

44819 

98218 

46601 

53399 

01782 

55181 

42 

19 

44862 

98215 

46648 

53352 

01785 

55138 

41 

20 

9.44905 

9.98211 

9.46694 

10.53306 

10.01789 

10.55095 

40 

21 

44948 

98207 

46741 

53259 

01793 

55052 

39 

22 

44992 

98204 

46788 

53212 

01796 

55008 

38 

23 

45035 

98200 

46835 

53165 

01800 

54965 

37 

24 

45077 

98196 

46881 

53119 

01804 

54923 

36 

25 

45120 

98192 

46928 

53072 

01808 

54880 

35 

26 

45163 

98189 

46975 

53025 

01811 

54837 

34 

27 

45206 

98185 

47021 

52979 

01815 

54794 

33 

28 

45249 

98181 

47068 

52932 

01819 

54751 

32 

29 

45292 

98177 

47114 

52886 

01823 

54708 

31 

30 

9.45334 

9.98174 

9.47160 

10.52840 

10.01826 

10.54666 

30 

31 

45377 

98170 

47207 

52793 

01830 

54623 

29 

32 

45419 

98166 

47253 

52747 

01834 

54581 

28 

1 33 

45462 

98162 

47299 

52701 

01838 

54538 

27 

34 

45504 

98159 

47346 

52654 

01841 

54496 

26 

35 

45547 

98155 

47392 

52608 

01845 

54453 

25 

36 

45589 

98151 

47438 

52562 

01849 

54411 

24 

37 

45632 

98147 

47484 

52516 

01853 

54368 

23 

38 

45674 

98144 

47530 

52470 

01856 

54326 

22 

39 

45716 

98140 

47576 

52424 

01860 

54284 

21 

40 

9.45758 

9.98136 

9-47622 

10.52378 

10.01864 

10.54242 

~2tT 

41 

45801 

98132 

47668 

52332 

01868 

54199 

19 

42 

45843 

98129 

47714 

52286 

01871 

54157 

18 

43 

45885 

98125 

47760 

52240 

01875 

54115 

17 

j 44 

45927 

98121 

47806 

52194 

01879 

54073 

16 

I 45 

45969 

98117 

47852 

52148 

01883 

54031 

15 

46 

46011 

98113 

47897 

52103 

01887 

53989 

14 

47 

46053 

98110 

47943 

52057 

01890 

53947 

13 

48 

46095 

98106 

47989 

52011 

01894 

53905 

12 

j 49 

46136 

98102 

48035 

51965 

01898 

53864 

11 

1 50 

9.46178 

9.98098 

9.48080 

10.51920 

10.01902 

10.53822 

~io 

51 

46220 

98094 

48126 

51874 

01906 

53780 

9 

| 52 

46262 

98090 

48171 

51829 

01910 

53738 

8 

53 

46303 

98087 

48217 

51783 

01913 

53697 

<r* 

i 

I 54 

46345 

98083 

48262 

51738 

01917 

53655 

6 

| 55 

46386 

98079 

48307 

51693 

01921 

53614 

5 

I 56 

46428 

98075 

48353 

51647 

01925 

53572 

4 

[ 57 

46469 

98071 

48398 

51602 

01929 

53531 

3 

| 58 

46511 

98067 

48443 

51557 

01933 

53489 

2 

S 59 

46552 

98063 

48489 

51511 

01937 

53448 

1 

I CO 

46594 

98060 

48534 

51466 

01940 

53406 

0 


Co-sine. 

Sine. 

Co-tang. 

Tangent. 

Co-secant 

Secant. 

IvT. 





















































































Artificial Sines, Tang, and Sec. 17 Degrees. 125 


|| 1V1. 

Sine. 

Co-sine. 

i'angent. 

Co-tang. 

Secant. 1 < 

Jo-secant 


11 0 

9.46594 

9.98060 

9.48534 

10.51466 

10.01940 

10.53406 

60 

i 1 

46635 

98056 

48579 

51421 

01944 

53365 

59 

H 2 

46676 

98052 

48624 

51376 

01948 

53324 

58 

1 3 

46717 

_ 98048 

48669 

51331 

01952 

53283 

57 

I 4 

46758 

98044 

48714 

51286 

01956 

53242 

56 

u ^ 

46800 

98040 

48759 

51241 

01960 

53200 

55 

H ® 

46841 

98036 

48804 

51196 

01964 

53159 

54 

] 7 

46882 

98032 

48849 

51151 

01968 

53118 

53 

' 3 

46923 

98029 

48894 

51106 

01971 

53077 

52 

9 

46964 

98025 

48939 

51061 

01975 

53036 

51 

U 10 

9.47005 

9.98021 

9.48984 

10.51016 

10.01979 

10.52995 

50 

11 

47045 

98017 

49029 

50971 

01983 

52955 

49 

L 12 

47086 

98013 

49073 

50927 

01987 

52914 

48 

L 13 

47127 

98009 

49118 

50882 

01991 

52873 

47 

14 

47168 

98005 

49163 

50837 

01995 

52832 

46 

I 15 

47209 

98001 

49207 

50793 

01999 

52791 

45 

1C 

47249 

97997 

49252 

50748 

02003 

52751 

44 

j 17 

47290 

97993. 

✓ 49296 

50704 

02007 

52710 

43 

j 18 

47330 

97989 

49341 

50659 

02011 

52670 

42 

19 

47371 

97986 

49385 

50615 

02014 

52629 

41 

I 20 

9.47411 

9.97982 

9.49430 

10.50570 

10.02018 

10.52589 

40 

j 21 

47452 

97978 

49474 

50526 

02022 

52548 

39 

22 

47492 

97974 

49519 

50481 

02026 

52508 

38 

1 23 

47533 

97970 

49563 

50437 

02030 

52467 

37 


47573 

97966 

49607 

50393 

02034 

52427 

36 

I 25 

4^613 

97962 

49652 

50348 

02038 

52387* 

35 

26 

47654 

97958 

49696 

50304 

02042 

52346 

34 

| 27 

47694 

97954 

49740 

50260 

02046 

52306 

33 

1 28 

47734 

97950 

49784 

50216 

02050 

52266 

32 

| 29 

47774 

97946 

49828 

50172 

02054 

52226 

31 

I 30 

9.47814 

9.97942 

9.49872 

10.50128 

10.02058 

10.52186 

30 

I 31 

47854 

97938 

49916 

50084 

02062 

52146 

29 

32 

47894 

97934 

49960 

50040 

02066 

52106 

28 

33 

47934 

97930 

50004 

49996 

02070 

52066 

27 

34 

47974 

97926 

50048 

49952 

02074 

52026 

26 

I 35 

48014 

97922 

50092 

49908 

02078 

51986 

25 

36 

48054 

97918 

50136 

49864 

02082 

51946 

24 , 

37 

48094 

97914 

50180 

49820 

02086 

51906 

/Vi * 

| 38 

48133 

97910 

50223 

49777 

02090 

51867 

22 

; 39 

48173 

97906 

50267 

49733 

02094 

51827 

21 

1 40 

9.48213 

9.97902 

9.50311 

10.49689 

10.02098 

10.51787 

20 

41 

48252 

97898 

50355 

49645 

02102 

51748 

19 

1 42 

48292 

97894 

50398 

49602 

02106 

51708 

18 

43 

48332 

97890 

50442 

49558 

02110 

51668 

17 

44 

48371 

97886 

50485 

49515 

02114 

51629 

16 

I 45 

48411 

97882 

50529 

49471 

02118 

51589 

15 

46 

48450 

97878 

50572 

49428 

02122 

51550 

14 

47 

48490 

97874 

50616 

49384 

02126 

51510 

13 

48 

48529 

97870 

50659 

49341 

02130 

51471 

12 

I 49 

48568 

97866 

50703 

49297 

02134 

51432 

11 

I 50 

9.48607 

9.97861 

9.50746 

10.49254 

10.02139 

10.51393 

10 

i 51 

48647 

97857 

50789 

49211 

02143 

51353 

9 

1 52 

48686 

97853 

50833 

49167 

02147 

51314 

8 

53 

48725 

97849 

50876 

49124 

02151 

51275 

7 

54 

48764 

97845 

50919 

49081 

02155 

51236 

6 

| 55 

48803 

97841 

50962 

49038 

02159 

51197 

5 

56 

48842 

97837 

51005 

48995 

02163 

51158 

4 

57 

48881 

97833 

51048 

48952 

02167 

51119 

C} 

O 

J 58 

48920 

97829 

51092 

48908 

02171 

51080 

2 

59 

48959 

97825 

51135 

48865 

02175 

51041 

1 

1 60 

48998 

97821 

51178 

48822 

02179 

51002 

0 

|ZL 

1 Co-sine. 

Sine. 

Co-tang. 

Tangent. 

Co-secant 

Secant. 

ivT 


72 Degrees. 
































































































12G Artificial Sines, Tang, and Sec. 18 Degrees. 


M. 

Sine. 

Co-sine. 

Tangent. 

Co-tang. 

Secant. 

Co-secant 


(J 

9.48998 

9.97821 

9.51178 

10.48822 

10.02179 

10.51002 

60 

1 

49037 

97817 

51221 

48779 

02183 

50963 

59 

2 

49076 

97812 

51264 

48736 

02188 

50924 

58 

3 

49115 

97808 

51306 

48694 

02192 

50885 

57 

4 

49153 

97804 

51349 

48651 

02196 

50847 

56 

5 

49192 

97800 

51392 

48608 

02200 

50808 

55 

6 

1 49231 

97796 

51435 

48565 

02204 

50769 

54 

7 

49269 

'97792 

51478 

48522 

02208 

50731 

53 

8 

49308 

97788 

51520 

48480 

02212 

50692 

52 

9 

49347 

97784 

51563 

48437 

02216 

50653 

51 

10 

9.49385 

9.97779 

9.51606 

10.48394 

10.02221 

10.50615 

50 

11 

49424 

97775 

51648 

48352 

02225 

50576 

49 

12 

49462 

97771 

51691 

48309 

02229 

50538 

48 

13 

49500 

97767 

51734 

48266 

02233 

50500 

47 

14 

49539 

97763 

51776 

48224 

02237 

50461 

46 

15 

49577 

97759 

51819 

48181 

02241 

50423 

45 

16 

49615 

97754 

51861 

48139 

02246 

50385 

44 

17 

49654 

97750 

51903 

48097 

02250 

50346 

43 

18 

49692 

97746 

51946 

48054 

02254 

50308 

42 

19 

49730 

97742 

51988 

48012 

02258 

50270 

41 

20 

9.49768 

9.97738 

9.52031 

10.47969 

10.02262 

10.50232 

40 

21 

49806 

97734 

52073 

47927 

02266 

50194 

39 

22 

49844 

97729 

52115 

47885 

02271 

50156 

38 

23 

49882 

97725 

52157 

47843 

02275 

50118 

37 

24- 

49920 

97721 

52200 

47800 

02279 

50080 

36 

25 # 

49958 

97717 

52242 

47758 

02283 

50042 

35 

26 

49996 

97713 

52284 

47716 

02287 

50004 

34 

27 

50034 

97708 

52326 

47674 

02292 

49966 

>53 

28 

50072 

97704 

52368 

47632 

02296 

49928 

32 

29 

50110 

97700 

52410 

47590 

02300 

49890 

31 

30 

9.50148 

9.97696 

9.52452 

10.47548 

10.02304 

10.49852 

30 

31 

50185 

97691 

52494 

47506 

02309 

49815 

29 

32 

50223 

97687 

52536 

47464 

02313 

49777 

28 

33 

50261 

97683 

52578 

47422 

02317 

49739. 

27 

34 

50298 

97679 

52620 

47380 

02321 

49702 

26 

35 

50336 

97674 

52661 

47339 

02326 

49664 

25 

36 

50374 

97670 

52703 

47297 

02330 

49626 

24 

37 

50411 

97666 

52745 

47255 

02334 

49589 

23 

38 

50449 

97662 

52787 

47213 

02338 

49551 

22 

39 

50486 

97657 

->,52829 

47171 

02343 

49514 

21 

40 

9.50523 

9.97653 

9.52870 

10.47130 

10.02347 

10.49477 

20 

41 

50561 

97649 

52912 

47088 

02351 

49439 

19 

42 

50598 

97645 

52953 

47047 

02355 

49402 

18 

43 

50635 

97640 

52995 

47005 

02360 

49365 

17 

44 

50673 

97636 

53037 

46963 

02364 

49327 

16 

45 

50710 

97632 

53078 

46922 

02368 

49290 

15 

46 

50747 

97628 

53120 

46880 

02372 

49253 

14 

47 

50784 

97623 

53161 

46839 

02377 

49216 

13 

48 

50821 

97619 

53202 

46798 

02381 

49179 

12 

49 

50858 

97615 

53244 

46756 

02385 

49142 

It 

50 

9.50896 

9.97610 

9.53285 

10.46715 

10.02390 

10.49104 

10 

51 

50933 

97606 

53327 

46673 

02394 

49067 

9 

52 

50970 

97602 

53368 

46632 

02398 

49030 

8 

53 

51007 

97597 

53409 

46591 

02403 

48993 

7 

54 

51043 

97593 

53450 

46550 

02407 

48957 

6 

55 

51080 

97589 

53492 

46508 

02411 

48920 

5 

56 

51117 

97584 

53533 

46467 

02416 

48883 

4 

57 

51154 

97580 

53574 

46426 

02420 

48846 

3 

58 

51191 

97576 

53615 

46385 

02424 

48809 

2 ; 

59 

51227 

97571 

53656 

46344 

02429 

48773 

i 

60 

51264 

97567 

53697 

46303 

02433 

48736 

0 < 


Cn-sine. 

Sine. 

Co-tang. 

Tangent.. 

('o-seeant 

Secant. 

M. j 





































































Artificial Sines, Tang, and Sec. 19 Degrees. 127 


M. 

Sine. 

Co-sine. 

Tangent. 

Co-tang. 

Secant. 

Co-secant 

— 

0 

9.51264 

9.97567 

9.53697 

10.46303 

10.02433 

10.48736 

60 

1 

51301 

97563 

53738 

46262 

02437 

48699 

59 

2 

51338 

97558 

53779 

46221 

02442 

48662 

58 

3 

51374 

97554 

53820 

46180 

02446 

48626 

57 

4 

51411 

97550 

53861 

46139 

02450 

48589 

56 

5 

51447 

97545 

53902 

46098 

02455 

48553 

55 

6 

51484 

97541 

53943 

46057 

02459 

48516 

54 

7 

51520 

97536 

53984 

46016 

02464 

48480 

53 

8 

51557 

97532 

54025 

45975 

02468 

48443 

52 

9 

51593 

97528 

54065 

45935 

02472 

48407 

51 

10 

9.51629 

9.97523 

9.54106 

10.45894 

10.02477 

10.48371 

50 

11 

51666 

97519 

54147 

45853 

02481 

48334 

49 

12 

51702 

97515 

54187 

45813 

02485 

48298 

48 

13 

51738 

97510 

54228 

45772 

02490 

48262 

47 

14 

51774 

97506 

54269 

45731 

02494 

48226 

46 

15 

51811 

97501 

54309 

45691 

02499 

48189 

45 

16 

51847 

97497 

54350 

45650 

02503 

48153 

44 

17 

51883 

97492 

54390 

45610 

02508 

48117 

43 

18 

51919 

97488 

54431 

45569 

02512 

48081 

42 

19 

51955 

97484 

54471 

45529 

02516 

48045 

41 

20 

9.51991 

9.97479 

9.54512 

10.45488 

10.02521 

10.48009 

40 

21 

52027 

97475 

54552 

45448 

02525 

47973 

39 

V 22 

52063 

97470 

54593 

45407 

02530 

47937 

38 

' 23 

52099 

97466 

54633 

45367 

02534 

47901 

37 

24 

52135 

97461 

54673 

45327 

02539 

47865 

36 

. 25 

52171 

97457 

54714 

45286 

02543 

47829 

35 

26 

52207 

97453 

54754 

45246 

02547 

47793 

34 

27 

52242 

97448 

54794 

45206 

02552 

47758 

33 

28 

52278 

97444 

54835 

45165 

02556 

47722 

32 

29 

52314 

97439 

54875 

45125 

02561 

47686 

31 

30 

9.52350 

9.97435 

9.54915 

10.45085 

10.02565 

10.47650 

30 

31 

52385 

97430 

54955 

45045 

02570 

47615 

29 

32 

52421 

97426 

54995 

45005 

02574 

47579 

28 

! 33 

52456 

97421 

55035 

44965 

02579 

47544 

27 

34 

52492 

97417 

55075 

44925 

02583 

47508. 

26 

35 

52527 

97412 

55115 

44885 

02588 

47473 

25 

] 36 

52563 

97408 

55155 

44845 

02592 

47437 

24 ‘ 

; 37 

52598 

97403 

55195 

44805 

02597 

47402 

23 

; 38 

52634 

97399 

55235 

44765 

02601 

47366 

22 

39 

52669 

97394 

55275 

44725 

02606 

47331 

21 

40 

9.52705 

9.97390 

9.55315 

10.44685 

10.02610 

10.47295 

20 

41 

52740 

97385 

55355 

44645 

02615 

47260 

19 

42 

52775 

97381 

55395 

44605 

02619 

47225 

18 

43 

52811 

97376 

55434 

44566 

02624 

47189 

17 

44 

52846 

97372 

55474 

44526 

02628 

47154 

16 

45 

52881 

97367 

55514 

44486 

02633 

47119 

15 

46 

52916 

97363 

55554 

44446 

02637 

47084 

14 

47 

52951 

97358 

55593 

44407 

02642 

47049 

13 

48 

52986 

97353 

55633 

44367 

02647 

47014 

12 

49 

53021 

97349 

55673 

44327 

02651 

46979 

11 

50 

9.53056 

9.97344 

9.55712 

10.44288 

10.02656 

10.46944 

10 

51 

53092 

97340 

55752 

44248 

02660 

46908 

9 

52 

53126 

97335 

55791 

44209 

02665 

46874 

6 

53 

53161 

97331 

55831 

44169 

02669 

46839 

7 

54 

53196 

97326 

55870 

44130 

02674 

46804 

6 

55 

53231 

97322 

55910 

44090 

02678 

46769 

5 

56 

53266 

97317 

55949 

44051 

02683 

46734 

4 

57 

53301 

97312 

55989 

44011 

02688 

46699 

3 

58 

53336 

97308 

56028 

43972 

02692 

46664 

2 | 

59 

53370 

97303 

56067 

43933 

02697 

46630 

1 

60 

53405 

97299 

,|,I07 

43893 

02701 

46595 

0 


Co-sine. 

Sine. 

Co-tang. 

Tangent. 1 

Co-secant. 

Secanl. 1 M. 


70 Degrees. 




















































































12i> 


Artificial Sines, Tang, and Sec. 20 Degrees. 


• - 

■ Vi. 

Sine. 

Co-sine. 

Tangent. 

Co-tang. 

Secant. 

Co-secant 


0 

9.53405 

9.97299 

9.56107 

10.43893 

10.02701 

10.46595 

60 

1 

53440 

97294 

56146 

43854 

02706 

46560 

59 

2 

53475 

97289 

56185 

43815 

02711 

46525 

58 

3 

53509 

97285 

56224 

43776 

02715 

46491 

57 

4 

53544 

97280 

56264 

43736 

02720 

46456 

56 

5 

53578 

97276 

56303 

43697 

02724 

46422 

55 

6 

53613 

97271 

56342 

43658 

02729 

46387 

54 

7 

53647 

97266 

56381 

43619 

02734 

46353 

53 

8 

53682 

97262 

56420 

43580 

02738 

46318 

52 

9 

53716 

97257 

56459 

43541 

02743 

46284 

51 

10 

9.53751 

9.97252 

9.56498 

10.43502 

10.02748 

10.46249 

50 

11 

53785 

97248 

56537 

43463 

02752 

46215 

49 

12 

53819 

97243 

56576 

43424 

02757 

46181 

48 

13 

53854 

97238 

56615 

43385 

02762 

46146 

47 

14 

53888 

97234 

56654 

43346 

02766 

46112 

46 

15 

53922 

97229 

56693 

43307 

02771 

46078 

45 

16 

53957 

97224 

56732 

43268 

02776 

46043 

44 

17 

53991 

97220 

56771 

43229 

02780 

46009 

43 

18 

54025 

97215 

56810 

43190 

02785 

45975 

42 

19 

54059 

97210 

56849 

43151 

02790 

45941 

41 

20 

9.54093 

9.97206 

9.56887 

10.43113 

10.02794 

10.45907 

40 

21 

54127 

97201 

56926 

43074 

02799 

45873 

39 

22 

54161 

97196 

56965 

43035 

02804 

45839 

38 

23 

54195 

97192 

57004 

42996 

02808 

45805 

37 

24 

54229 

97187 

57042 

42958 

02813 

45771 

36 

25 

54263 

97182 

57081 

42919 

02818 

45737 

35 

26 

54297 

97178 

57120 

42880 

02822 

45703 

34 

27 

54331 

97173 

57158 

42842 

02827 

45669 

33 

28 

54365 

97168 

57197 

42803 

02832 

45635 

32 

29 

54399 

97163 

57235 

42765 

02837 

45601 

31 

30 

9.54433 

9.97159 

9.57274 

10.42726 

10.02841 

10.45567 

30 

31 

54466 

97154 

57312 

42688 

02846 

45534 

29 

32 

54500 

97149 

57351 

42649 

02851 

45500 

23 

.33 

54534 

97145 

57389 

42611 

02855 

45466 

27 

34 

54567 

97140 

57428 

42572 

02860 

45433 

26 

35 

54601 

97135 

57466 

42534 

02865 

45399 

25 

36 

54635 

97130 

57504 

42496 

02870 

45365 

24 

37 

54668 

97126 

57543 

42457 

02874 

45332 

23 

38 

54702 

97121 

• 57581 

42419 

02879 

45298 

22 

39 

54735 

97116 

57619 

42381 

02884 

45265 

21 

40 

9.54769 

9.97111 

9.57658 

10.42342 

10.02889 

10.45231 

20 

41 

54802 

97107 

57696 

42304 

02893 

45198 

19 

42 

54836 

97102 

57734 

42266 

02898 

45164 

. 18 

43 

54869 

97097 

57772 

42228 

02903 

45131 

17 

44 

54903 

97092 

57810 

42190 

02908 

45097 

16 

45 

54936 

97087 

57849 

42151 

02913 

45064 

15 

46 

54969 

97083 

57887 

42113 

02917 

45031 

14 

47 

55003 

97078 

57925 

42075 

02922 

44997 

13 

48 

55036 

97073 

57963 

42037 

02927 

44964 

12 

49 

55069 

97068 

58001 

41999 

02932 

44931 

11 

50 

9.55102 

9.97063 

9.58039 

10.41961 

10.02937 

10.44898 

10 

51 

55136 

97059 

58077 

41923 

02941 

44864 

9 

52 

55169 

97054 

58115 

41885 

02946 

44831 

8 

53 

55202 

97049 

58153 

41847 

02951 

44798 

7 

54 

55235 

97044 

58191 

41809 

02956 

44765 

6 

55 

55268 

97039 

58229 

41771 

02961 

44732 

5 

56 

55301 

97035 

58267 

41733 

02965 

44699 

4 

57 

.55334 

97030 

58304 

41696 

02970 

44666 

3 

58 

55367 

97025 

58342 

41658 

02975 

44633 

2 

59 

55400 

97020 

58380 

41620 

02980 

44600 

1 

60 

55133 

97015 

58418 

41582 

02985 

44567 

0 


('o-sine. 

Sine. 

Co-tang. 

Tangent. 

Co-secant 

Secant. 

M. 


69 Degrees. 
























































































Artificial Sines, Tang, and Sec. 21 Degrees. 129 


M. 

Sine. 

Co-sine. 

Tangent. 

Co-tang. 

Secant. | 

Co-secant 


0 

9•55433 

9.97015 

9.58418 

10.41582 

10.02985 

10.44567 

60 

1 

55466 

97010 

58455 

41545 

02990 

44534 

59 

2 

55499 

97005 

58493 

41507 

02995 

44501 

58 

3 

55532 

97001 

58531 

41469 

02999 

44468 

57 

4 

55564 

96996 

58569 

41431 

03004 

44436 

56 

5 

55597 

96991 

58606 

41394 

03009 

44403 

55 

6 

55630 

96986 

58644 

41356 

03014 

44370 

54 

7 

55663 

96981 

58681 

41319 

03019 

44337 

53 

8 

55695 

96976 

58719 

41281 

03024 

44305 

52 

9 

55728 

96971 

58757 

41243 

03029 

44272 

51 

10 

9.55761 

9.96966 

9.58794 

10.41206 

10.03034 

10.44239 

50 

11 

55793 

96962 

58832 

41168 

03038 

44207 

49 

12 

55826 

96957 

58869 

41131 

03043 

44174 

48 

13 

55858 

96952 

58907 

41093 

03048 

44142 

47 

14 

55891 

96947 

58944 

41056 

03053 

44109 

46 

15 

55923 

96942 

58981 

41019 

03058 

44077 

45 

16 

55956 

96937 

59019 

40981 

03063 

44044 

44 

17 

55988 

96932 

59056 

40944 

03068 

44012 

43 

18 

56021 

96927 

59094 

40906 

03073 

43979 

42 

19 

56053 

96922 

59131 

40869 

03078 

43947 

41 

20 

9.56085 

9.96917 

9.59168 

10.40832 

10.03083 

10.43915 

40 

21 

56118 

96912 

59205 

40795 

03088 

43882 

39 

22 

56150 

96907 

59243 

40757 

03093 

43850 

38 

23 

56182 

96903 

59280 

40720 

03097 

43818 

37 

24 

56215 

96898 

59317 

40683 

03102 

43785 

36 

25 

56247 

96893 

59354 

40646 

03107 

43753 

35 

26 

56279 

96888 

59391 

40609 

03112 

43721 

34 

27 

56311 

96883 

59429 

40571 

03117 

43689 

33 

28 

56343 

96878 

59466 

40534 

03122 

43657 

32 

1 29 

56375 

96873 

59503 

40497 

03127 

43625 

31 

30 

9.56408 

9.96868 

9.59540 

10.40460 

10.03132 

10.43592 

30 

31 

56440 

96863 

59577 

40423 

03137 

43560 

29 

32 

56472 

96858 

59614 

40386 

03142 

43528 

28 

33 

56504 

96853 

59651 

40349 

03147 

43496 

27 

34 

56536 

96848 

59688 

40312 

03152 

43464 

26 

35 

56568 

96843 

59725 

40275 

03157 

43432 

25 

36 

56599 

96838 

59762 

40238 

03162 

43401 

24 

37 

56631 

96833 

59799 

40201 

03167 

43369 

23 

38 

56663 

96828 

59835 

40165 

* 03^72 

43337 

22 

39 

56695 

96823 

59872 

40128 

*• * 03177 

43305 

21 

40 

9.56727 

9.96818 

9.59909 

10.40091 

10.03182 

10.43273 

20 

41 

56759 

96813 

59946 

40054 

03187 

43241 

19 

42 

56790 

96808 

59983 

40017 

03192 

43210 

18 

43 

56822 

96803 

60019 

39981 

03197 

43178 

17 

44 

56854 

96798 

60056 

39944 

03202 

43146 

16 

45 

56886 

96793 

60093 

39907 

03207 

43114 

15 

46 

56917 

96788 

60130 

39870 

03212 

43083 

14 

47 

56949 

96783 

60166 

39834 

03217 

43051 

13 

48 

56980 

96778 

60203 

39797 

03222 

43020 

12 

49 

57012 

96772 

60240 

39760 

03228 

42988 

11 

50 

9.57044 

9.96767 

9.60276 

10.39724 

10.03233 

10.42956 

10 

51 

57075 

96762 

60313 

39687 

03238 

42925 

9 

52 

57107 

96757 

60349 

39651 

03243 

42893 

8 

53 

57138 

96752 

60386 

39614 

03248 

42862 

7 

54 

57169 

96747 

60422 

39578 

03253 

42831 

6 

55 

57201 

96742 

60459 

39541 

03258 

42799 

5 

56 

57232 

96737 

60495 

39505 

03263 

42768 

4 

57 

57264 

96732 

60532 

39468 

03268 

42736 

-> 

58 

57295 

96727 

\ 60568 

39432 

03273 

42705 

2 

59 

57326 

96722 

60605 

39395 

03278 

42674 


60 

57358 

96717 

60641 

39359 

03283 

42642 


| Co-sine. 

Sine. 

1 Co-tang. 

| Tangent. 

Co-secant 

Secant. 

M. 

—■ r-frJ 


R 68 Degrees^ 










































































130 Artificial Sines, Tang, and Sec. 22 Degrees.. 


I M. 

Sine. 

Co-sine. 

Tangent. 1 

Co-tang. 

Secant. 

Co-secant 


0 

9.57358 

9.96717 

9.60641 

10.39359 

10.03283 

10.42642 

60 

1 1 

57389 

96711 

60677 

39323 

03289 

42611 

59 

2 

57420 

96706 

60714 

39286 

03294 

42580 

58 

3 

57451 

96701 

60750 

39250 

03299 

42549 

57 

4 

57482 

96696 

60786 

39214 

03304 

42518 

56 

5 

57514 

96691 

60823 

39177 

03309 

42486 

55 

6 

57545 

96686 

60859 

39141 

03314 

42455 

54 

7 

57576 

96681 

60895 

39105 

03319 

42424 

53 

8 

57607 

96676 

60931 

39069 

03324 

42393 

52 

9 

57638 

96670 

60967 

39033 

03330 

42362 

51 

10 

9.57669 

9.96665 

9.61004 

10.38996 

10.03335 

10.42331 

50 

11 

57700 

96660 

61040 

38960 

03340 

42300 

49 

12 

57731 

96655 

61076 

38924 

03345 

42269 

48 

13 

57762 

96650 

61112 

38888 

03350 

42238 

47 

14 

57793 

96645 

61148 

38852 

03355 

42207 

46 

15 

57824 

96640 

61184 

38816 

03360 

42176 

45 

16 

57855 

96634 

61220 

38780 

03366 

42145 

44 

17 

57885 

96629 

61256 

38744 

03371 

42115 

43 

18 

57916 

96624 

61292 

38708 

03376 

42084 

42 

19 

57947 

96619 

61328 

38672 

03381 

42053 

41 

20 

9.57978 

9.96614 

9.61364 

10.38636 

10.03386 

10.42022 

40 

21 

58008 

96608 

61400 

38600 

03392 

41992 

39 

22 

58039 

96603 

61436 

38564 

03397 

41961 

38 

23 

58070 

96598 

61472 

38528 

03402 

41930 

37 

24 

58101 

96593 

61508 

38492 

03407 

41899 

36 

25 

58131 

96588 

61544 

38456 

03412 

41869 

35 

26 

58162 

96582 

61579 

38421 

03418 

41838 

34 

27 

58192 

96577 

61615 

38385 

03423 

41808 

33 

28 

58223 

96572 

61651 

38349 

03428 

41777 

32 

29 

58253 

96567 

61687 

38313 

03433 

41747 

31 

30 

9.58284 

9.96562 

9.61722 

10.38278 

10.03438 

10.41716 

30 

31 

58314 

96556 

61758 

38242 

03444 

41686 

29 

32 

58345 

96551 

61794 

38206 

03449 

41655 

28 

33 

58375 

96546 

61830 

38170 

03454 

41625 

27 

34 

58406 

96541 

61865 

38135 

03459 

41594 

26 , 

35 

58436 

96535 

61901 

38099 

03465 

41564 

25 

36 

58467 

96530 

61936 

38064 

03470 

41533 

24 

37 

58497 

96525 

61972 

38028 

03475 

41503 

23 

38 

58527 

965^0. 

62008 

37992 

03480 

41473 

22 

39 

58557 

96514 

62043 

37957 

03486 

41443 

21 

40 

9.58588 

9.96509 

9.62079 

10.37921 

10.03491 

10.41412 

20 

41 

58618 

96504 

62114 

37886 

03496 

41382 

19 

42 

58648 

96498 

62150 

37850 

03502 

41352 

18 

43 

58678 

96493 

62185 

37815 

03507 

41322 

17 

44 

58709 

96488 

62221 

37779 

03512 

41291 

16 

45 

58739 

96483 

62256 

37744 

*03517 

41261 

15 

46 

58769 

96477 

62292 

37708 

03523 

41231 

14 

47 

58799 

96472 

62327 

37673 

03528 

41201 

13 

48 

58829 

96467 

62362 

37638 

03533 

41171 

12 

49 

58859 

9646; 

62398 

37602 

03539 

41141 

11 

4o 

9.58889 

9.96456 

9.62433 

10.37567 

10.03544 

10.41111 

~w 

51 

58919 

96451 

62468 

37532 

03549 

41081 

9 

52 

58949 

96445 

62504 

37496 

03555 

41051 

8 

53 

58979 

96440 

62539 

37461 

03560 

41021 

7 

54 

59009 

96435 

62574 

37426 

03565 

40991 

6 

55 

69039 

96429 

62609 

37391 

03571 

40961 

5 

56 

59069 

96424 

62645 

37355 

03576 

40931 

4 

57 

59098 

96419 

62680 

37320 

03581 

40902 

3 

58 

59128 

96413 

62715 

37285 

03587 

40872 

2 

59 

59158 

96408 

62750 

37250 

03592 

40842 

1 

60 

59188 

96403 

62785 

37215 

03597 

40812 

0 


Go-sine. 

Sine. 

Co-tang. 

Tangent. 

Co-secant 

Secant. 

M. 


67 Degrees 


i 4 




























































































Artificial Sines, Tang, and Sec. 23 Degrees. 131 


M. 

Sine. 

Co-sine. 

| Tangent. 

| Co-tang. 

Secant. 

Co-secant 1 

0 

9.59188 

9.96403 

9.62785 

10.37215 

10.03597 

10.40812 

60 

I 1 

59213 

96397 

62820 

37180 

03603 

40782 

59 

£ 2 

59247 

96392 

62855 

37145 

03608 

40753 

58 

1 3 

59277 

96387 

62890 

37110 

03613 

40723 

57 

4 

59307 

96381 

62926 

37074 

03619 

40693 

56 

5 

59336 

96376 

62961 

37039 

03624 

40664 

55 

! 6 

59366 

96370 

62996 

37004 

03630 

40634 

54 

I 7 

59396 

96365 

63031 

36969 

03635 

40604 

53 

8 

59425 

96360 

63066 

36934 

03640 

40575 

52 

] 9 

59455 

96354 

63101 

36899 

03646 

40545 

51 

1 10 

9.59484 

9.96349 

9.63135 

10.36865 

10.03651 

10.40516 

50 

1 11 

59514 

96343 

63170 

36830 

03657 

40486 

49 

1 12 

59543 

96338 

63205 

36795 

03662 

40457 

48 

1 13 

59573 

96333 

63240 

36760 

03667 

40427 

47 

1 14 

59602 

96327 

63275 

36725 

03673 

40398 

46 

I 15 

59632 

96322 

63310 

36690 

03678 

40368 

45 

16 

59661 

96316 

63345 

36655 

03684 

40339 

44 

| 17 

59690 

96311 

63379 

36621 

03689 

40310 

43 

1 13 

59720 

96305 

63414 

36586 

03695 

40280 

42 

\ 19 

59749 

96300 

63449 

36551 

03700 

40251 

41 

20 

9.59778 

9.96294 

9.63484 

10.36516 

10.03706 

10.40222 

40 

I 21 

59808 

96289 

63519 

36481 

03711 

40192 

39 

22 

59837 

96284 

63553 

36447 

03716 

40163 

38 

23 

59366 

96278 

63588 

36412 

03722 

40134 

37 

24 

59895 

96273 

63623 

36377 

03727 

40105 

36 

25 

59924 

96267 

63657 

36343 

03733 

40076 

35 

26 

59954 

96262 

63692 

36308 

03738 

40046 

34 

27 

59983 

96256 

63726 

36274 

03744 

40017 

33 

28 

60012 

96251 

63761 

36239 

03749 

39988 

32 

29 

60041 

96245 

63796 

36204 

03755 

39959 

31 

30 

9.60070 

9.96240 

9.63830 

10.36170 

10.03760 

10.39930 

30 

31 

60099 

96234 

63865 

36135 

03766 

39901 

29 

32 

60128 

96229 

63899 

36101 

03771 

39872 

28 

33 

60157 

96223 

63934 

36066 

03777 

39843 

27 

34 

60186 

96218 

63968 

36032 

03782 

39814 

26 

35 

60215 

96212 

64003 

35997 

03788 

39785 

25 

36 

60244 

96207 

64037 

35963 

03793 

39756 

24 

t 37 

60273 

96201 

64072 

35928 

03799 

39727 

23 

38 

60302 

96196 

64106 

35894 

03804 

39698 

22 

39 

60331 

96190 

64140 

35860 

03810 

39669 

21 

40 

9.60359 

9.96185 

9.64175 

10.35825 

10.03815 

10.39641 

20 

41 

60388 

96179 

64209 

35791 

03821 

39612 

19 

42 

60417 

96174 

64243 

35757 

03826 

39583 

18 

43 

60446 

96168 

64278 

35722 

03832 

39554 

17 

44 

60474 

96162 

64312 

35688 

03838 

39526 

16 

45 

60503 

96157 

64346 

35654 

03843 

39497 

15 

46 

60532 

96151 

64381 

35619 

03849 

39468 

14 

47 

60561 

96146 

64415 

35585 

03854 

39439 

13 

48 

60589 

96140 

64449 

35551 

03860 

39411 

12 

49 

60618 

96135 

64483 

35517 

03865 

39382 

11 

50 

9.60646 

9.96129 

9.64517 

10.35483 

10.03871 

10.39354 

10 

51 

60675 

96123 

64552 

35448 

03877 

39325 

9 

52 

60704 

96118 

64586 

35414 

03882 

39296 

8 

53 

60732 

96112 

64620 

35380 

03888 

39268 

7 

54 

60761 

96107 

64654 

35346 

03893 

39239 

6 

55 

60789 

96101 

64688 

35312 

03899 

39211 

5 

56 

60818 

96095 

64722 

35278 

03905 

39182 

4 

57 

60846 

96090 

64756 

35244 

03910 

39154 

3 

58 

60875 

96084 

64790 

35210 

03916 

39125 

2 

59 

60903 

96079 

64824 

35176 

03921 

39097 

1 

60 

60931 

96073 

64858 

35142 

03927 

39069 

0 


Co-sine. 

Sine. 

Co-tang. 

Tangent. 

Co-secant 

Secant. I 

M. 1 


G6 Degrees 















































































132 Artificial Sines, Tang, and Sec. 24 Degrees. 


M. 

Sine. 

Co-sine. 

Tangent. 

Co-tang. 

Secant. | 

Co-secant 


0 

9.60931 

9.96073 

9.64858 

10.35142 

10.03927 

10.39069 

60 

1 

60960 

96067 

64892 

35108 

03933 

39040 

59 

2 

60988 

96062 

64926 

35074 

03938 

39012 

58 

3 

61016 

96056 

64960 

35040 

03944 

38984 

57 

4 

61045 

96050 

64994 

35006 

03950 

38955 

56 

5 

61073 

96045 

65028 

34972 

03955 

38927 

55 

6 

61101 

96039 

65062 

34938 

03961 

38899 

54 

7 

61129 

96034 

65096 

34904 

03966 

38871 

53 

8 

61158 

96028 

65130 

34870 

03972 

38842 

52 

9 

61186 

96022 

65164 

34836 

03978 

38814 

51 

10 

9.61214 

9.96017 

9.65197 

10.34803 

10.03983 

10.38786 

50 

11 

61242 

96011 

65231 

34769 

03989 

38758 

49 

12 

61270 

96005 

65265 

34735 

03995 

38730 

48 

13 

61298 

96000 

65299 

34701 

04000 

38702 

47 

14 

61326 

95994 

65333 

34667 

04006 

38674 

46 

15 

61354 

95988 

65366 

34634 

04012 

38646 

45 

16 

61382 

95982 

65400 

34600 

04018 

38618 

44 

17 

61411 

95977 

65434 

34566 

04023 

38589 

43 

18 

61438 

95971 

65467 

34533 

04029 

38562 

42 

19 

61466 

95965 

65501 

34499 

04035 

38534 

41 

20 

9.61494 

9.95960 

9.65535 

10.34465 

10.04040 

10.38506 

40 

21 

61522 

95954 

65568 

34432 

04046 

38478 

39 

22 

61550 

95948 

65602 

34398 

04052 

38450 

38 

23 

61578, 

95942 

65636 

34364 

04058 

38422 

37 

24 

61606 

95937 

65669 

34331 

04063 

38394 

36 

25 

61634 

95931 

65703 

34297 

04069 

38366 

35 

26 

61662 

95925 

65736 

34264 

04075 

38338 

34 j 

27 

61689 

95920 

65770 

34230 

04080 

38311 

33 j 

28 

61717 

95914 

65803 

34197 

04086 

38283 

32 

29 

61745 

95908 

65837 

34163 

04092 

38255 

31 

30 

9.61773 

9.95902 

9.65B70 

10.34130 

10.04098 

10.38227 

30 

31 

61800 

95897 

65904 

34096 

04103 

38200 

29 

32 

61828 

95891 

65937 

34063 

04109 

38172 

28 

33 

61856 

95885 

65971 

34029 

04115 

38144 

27 

34 

61883 

95879 

66004 

33996 

04121 

38117 

26 

35 

61911 

95873 

66038 

33962 

04127 

38089 

25 

36 

61939 

95868 

66071 

33929 

04132 

38061 

24 

37 

61966 

95862 

66104 

33896 

04138 

38034 

23 

38 

61994 

95856 

66138 

33862 

04144 

38006 

22 

39 

62021 

95850 

66171 

33829 

04150 

37979 

21 

: 40 

9.62049 

9.95844 

9.66204 

10.33796 

10.04156 

10.37951 

20 

41 

62076 

95839 

66238 

33762 

04161 

37924 

19 

42 

62104 

95833 

66271 

33729 

04167 

37896 

18 

43 

62131 

95827 

66304 

33696 

04173 

37869 

17 

44 

62159 

95821 

66337 

33663 

04179 

37841 

16 

45 

62186 

95815 

66371 

33629 

04185 

37814 

15 

46 

62214 

95810 

66404 

33596 

04190 

37786 

14 

47 

62241 

95804 

66437 

33563 

04196 

37759 

13 

48 

62268 

95798 

66470 

33530 

04202 

37732 

12 

49 

62296 

95792 

66503 

33497 

04208 

37704 

11 

50 

9.62323 

9.95786 

9.66537 

10.33463 

10.04214 

10.37677 

10 

51 

62350 

95780 

66570 

33430 

04220 

37650 

9 

52 

62377 

95775 

66603 

33397 

04225 

37623 

8 

53 

62405 

95769 

66636 

33364 

04231 

37595 

7 

54 

62432 

95763 

66669 

33331 

04237 

37568 

6 

55 

62459 

95757 

66702 

33298 

04243 

37541 

5 

56 

62486 

95751 

66735 

33265 

04249 

37514 

4 

57 

62513 

95745 

66768 

33232 

’04255 

37487 

3 

< 58 

62541 

95739 

66801 

33199 

04261 

37459 

2 

•59 

62568 

95733 

66834 

33166 

04267 

37432 

1 

60 

62595 

95728 

66867 

33133 

04272 

37405 

0 


{ o-sine. 

Sine. 

Co-tang. 

Tangent. 

Co-secant 

Secant. 

IVT. 


65 Degrees 





















































































Artificial Sines, Tang, and Sec. 25 Degrees. 133 


M. 

Sine. 

Co-sine. 

Tangent, j 

Co-tang. 

Secant. 

Co-secant 


0 

9.62595 

9.95728 

9.66867 

10.33133 

10.04272 

10.37405 

60 

1 

62622 

95722 

66900 

33100 

04278 

37378 

59 

2 

62649 

95716 

66933 

33067 

04284 

37351 

58 

3 

62676 

95710 

66966 

33034 

04290 

37324 

57 

4 

62703 

95704 

66999 

33001 

. 04296 

37297 

56 

5 

62730 

95698 

67032 

32968 

■* 04302 

37270 

55 

6 

62757 

95692 

67065 

32935 

04308 

37243 

54 

7 

62784 

95686 

67098 

32902 

04314 

37216 

53 

8 

62811 

95680 

67131 

32869 

04320 

37189 

52 

9 

62838 

95674 

67163 

32837 

04326 

37162 

51 

10 

9.62865 

9.95668 

9.67196 

10.32804 

10.04332 

10.37135 

50 

11 

62892 

95663 

67229 

32771 

04337 

37108 

49 

12 

62918 

95657 

67262 

32738 

04343 

37082 

48 

13 

62945 

95651 

67295 

32705 

04349 

37055 

47 

14 

62972 

95645 

67327 

32673 

04355 

37028 

46 

15 

62999 

9^639 

67360 

32640 

04361 

37001 

45 

10 

63026 

"95633 

67393 

32607 

04367 

36974 

44 

17 

63052 

95627 

67426 

32574 

04373 

36948 

43 

18 

63079 

95621 

67458 

32542 

04379 

36921 

42 

19 

63106 

95615 

67491 

32509 

04385 

36894 

41 

20 

9.63133 

9.95609 

9.67524 

10.32476 

10.04391 

10.36867 

40 

21 

63159 

95603 

67556 

32444 

04397 

36841 

39 

22 

63186 

95597 

67589 

32411 

04403 

36814 

38 

23 

63213 

95591 

67622 

32378 

04409 

36787 

37 

24 

63239 

95585 

67654 

32346 

04415 

36761 

36 

25 

63266 

95579 

67687 

32313 

04421 

36734 

35 

26 

63292 

95573 

67719 

32281 

04427 

36708 

34 

27 

63319 

95567 

67752 

32248 

04433 

36681 

33 

28 

63345 

95561 

67785 

32215 

04439 

36655 

32 

29 

63372 

95555 

67817 

32183 

04445 

36628 

31 

30 

9.63398 

9.95549 

9.67850 

10.32150 

10.04451 

10.36602 

30 

31 

63425 

95543 

67882 

32118 

04457 

36575 

29 

32 

63451 

95537 

67915 

32085 

04463 

36549 

28 

33 

63478 

95531 

67947 

32053 

04469 

36522 

27 

34 

63504 

95525 

67980 

32020 

04475 

36496 

26 

35 

63531 

95519 

68012 

31988 

04481 

36469 

25 

36 

63557 

95513 

68044 

31956 

04487 

36443 

24 

37 

63583 

95507 

68077 

31923 

04493 

36417 

23 

38 

63610 

95500 

68109 

31891 

04500 

36390 

22 

39 

63636 

95494 

68142 

31858 

04506 

36364 

21 

40 

9.63662 

9.95488 

9.68174 

10.31826 

10.04512 

10.36338 

20 

41 

63689 

95482 

68206 

31794 

04518 

36311 

19 

42 

63715 

95476 

68239 

31761 

04524 

36285 

18 

43 

63741 

95470 

68271 

31729 

04530 

36259 

17 

44 

63767 

95464 

68303 

31697 

04536 

36233 

16 

45 

63794 

95458 

63336 

31664 

04542 

36206 

15 

46 

63820 

95452 

68368 

31632 

04548 

36180 

14 

47 

63846 

95446 

68400 

31600 

04554 

36154 

13 

48 

63872 

95440 

68432 

31568 

04560 

36128 

12 

49 

63898 

95434 

68465 

31535 

04566 

36102 

11 

50 

9.63924 

9.95427 

9.68497 

10.31503 

10.04573 

10.36076 

10 

51 

63950 

95421 

68529 

31471 

04579 

36050 

9 

52 

63976 

95415 

68561 

31439 

04585 

36024 

8 

53 

64002 

95409 

68593 

31407 

04591 

35998 

7 

! 54 

64028 

95403 

68626 

31374 

04597 

35972 

6 

55 

64054 

95397 

68658 

31342 

04603 

35946 

5 

' 56 

64080 

95391 

68690 

31310 

04609 

35920 

4 

57 

64106 

95384 

68722 

31278 

04616 

35894 

3 

58 

64132 

95378 

'68754 

31246 

04622 

35868 

2 

59 

64158 

95372 

68786 

31214 

04628 

35842 

1 

60 

64184 

95366 

68818 

31182 

04634 

35816 

0 

1 Co-sinc. 

Sine. 

Co-tang. 

Tangent. 

Co-secant 

Secant. 

M. 


64 Degrees 











































































134 Artificial Sines, Tang, and Sec. 26 Degrees. 


M. 

Sine. 

Co-sine. 

Tangent. 

Co-tang. 

Secant. 

Co-secant 


0 

9.64184 

9.95366 

9.68818 

10.31182 

10.04634 

10.35816 

60 

1 

64210 

95360 

68850 

31150 

04640 

35790 

59 

2 

64236 

95354 

68882 

31118 

04646 

35764 

58 

3 

64262 

95348 

68914 

31086 

04652 

35738 

57 

4 

64288 

95341 

68946 

31054 

04659 

35712 

56 

5 

64313 

95335 

68978 

31022 

04665 

35687 

55 

6 

64339 

95329 

69010 

30990 

04671 

35661 

54 

7 

64365 

95323 

69042 

30958 

04677 

35635 

53 

8 

64391 

95317 

69074 

30926 

04683 

35609 

52 

9 

64417 

95310 

69106 

30894 

04690 

35583 

"51 

10 

9.64442 

9.95304 

9.69138 

10.30862 

10.04696 

10.35558 

50 

11 

64468 

95298 

69170 

30830 

04702 

35532 

49 

12 

64494 

95292 

69202 

30798 

04708 

35506 

48 

13 

64519 

95286 

69234 

30766 

04714 

35481 

47 

14 

64545 

95279 

69266 

30734 

04721 

35455 

46 

15 

64571 

95273 

69298 

30702 

04727 

35429 

45 

16 

64596 

95267 

69329 

30671 

04733 

35404 

44 

17 

64622 

95261 

69361 

30639 

04739 

35378 

43 

18 

64647 

95254 

69393 

30607 

04746 

35353 

42 

19 

64673 

95248 

69425 

30575 

04752 

35327 

41 

20 

9.64698 

9.95242 

9.69457 

10.30543 

10.04758 

10.35302 

40 

21 

64724 

95236 

69488 

30512 

04764 

35276 

39 

22 

64749 

95229 

69520 

30480 

04771 

35251 

38 

23 

64775 

95223 

69552 

30448 

04777 

35225 

37 

‘ 24 

64800 

95217 

69584 

30416 

04783 

35200 

36 

25 

64826 

95211 

69615 

30385 

04789 

35174 

35 

26 

64851 

95204 

69647 

30353 

04796 

35149 

34 

27 

64877 

95198 

69679 

30321 

04802 

35123 

33 

28 

64902 

95192 

69710 

30290 

04808 

35098 

32 

29 

64927 

95185 

69742 

30258 

04815 

35073 

31 

30 

9.64953 

9.95179 

9.69774 

10.30226 

10.04821 

10.35047 

30 

31 

64978 

95173 

69805 

30195 

04827 

35022 

29 

32 

65003 

95167 

69837 

30163 

04833 

34997 

28 

33 

65029 

95160 

69868 

30132 

04840 

34971 

27 

34 

65054 

95154 

69900 

30100 

04846 

34946 

26 

35 

65079 

95148 

69932 

30068 

04852 

34921 

25 

36 

65104 

95141 

69963 

30037 

04859 

34896 

24 

37 

65130 

95135 

69995 

30005 

04865 

34870 

23 

38 

65155 

95129 

70026 

29974 

04871 

34845 

22 

39 

65180 

95122 

70058 

29942 

04878 

34820 

21 

40 

9.65205 

9.95116 

9.70089 

10.29911 

10.04884 

10.34795 

20 

41 

65230 

95110 

70121 

29879 

04890 

34770 

19 

42 

65255 

95103 

70152 

29848 

04897 

34745 

18 

43 

65231 

95097 

70184 

29816 

04903 

34719 

17 

44 

65306 

95090 

70215 

29785 

04910 

34694 

16 

45 

65331 

95084 

70247 

29753 

04916 

34669 

15 

46 

65356 

95078 

70278 

29722 

04922 

34644 

14 

47 

65381 

95071 

70309 

29691 

04929 

34619 

13 

48 

65406 

95065 

70341 

29659 

04935 

34594 

12 

49 

65431 

95059 

70372 

29628 

04941 

34569 

11 

50 

9.65456 

9.95052 

9.70404 

10.29596 

10.04948 

10.34544 

10 

51 

65481 

95046 

70435 

29565 

04954 

34519 

9 

52 

65506 

95039 

70466 

29534 

04961 

34494 

8 

53 

65531 

95033 

70498 

29502 

04967 

34469 

7 

54 

65556 

95027 

70529 

29471 

04973 

34444 

6 

55 

65580 

95020 

70560 | 

29440 

04980 

34420 

5 

56 

65605 

95014 

70592 

29408 

04986 

34395 

4 

57 

65630 

95007 

70623 1 

29377 

04993 

34370 

3 

58 

65655 

95001 

70654 1 

29346 

04999 

34345 

2 

59 

65680 

94995 

70685 

29315 

05005 

34320 

1 

60 

65705 

94988 

70717 

29283 

05012 

34295 

0 


Co-sine. 

Sine. 

Co-tang. 

Tangent. 

Co-secant I 

Secant. 

M. 


* 


63 Degrees 


















































































Artificial Sines, Tang, and Sec. 27 Degrees. 135, 


M. 

Sine. 

Co-sine. 

1 Tangent. 

I Co-tang. 

Secant. 

Co-secant 


0 

9.65705 

9.94988 

9.70717 

10.29283 

10.05012 

10.34295 

60 

1 

65729 

94982 

70748 

29252 

05018 

34271 

59 

2 

65754 

94975 

70779 

29221 

05025 

34246 

58 

3 

65779 

94969 

70810 

29190 

05031 

34221 

57 

4 

65804 

94962 

70841 

29159 

05038 

34196 

56 

5 

65828 

94956 

70873 

29127 

05044 

34172 

55 

6 

65853 

94949 

70904 

29096 

05051 

34147 

54 

7 

65878 

94943 

70935 

29065 

05057 

34122 

53 

8 

65902 

94936 

70966 

29034 

05064 

34098 

52 

9 

65927 

94930 

70997 

29003 

05070 

34073 

51 

10 

9.65952 

9.94923 

9.71028 

10.28972 

10.05077 

10.34048 

50 

11 

65976 

94917 

71059 

28941 

05083 

34024 

49 

12 

66001 

94911 

71090 

28910 

05089 

33999 

48 

13 

66025 

94904 

71121 

28879 

05096 

33975 

47 

14 

66050 

94898 

71153 

28847 

05102 

33950 

46 

15 

66075 

94891 

71184 

28816 

05109 

33925 

45 

16 

66099 

94885 

71215 

28785 

05115 

33901 

44 

17 

66124 

94878 

71246 

28754 

05122 

33876 

43 

18 

66148 

94871 

71277 

28723 

05129 

33852 

42 

19 

66173 

94865 

71308 

28692 

05135 

33827 

41 

20 

9.66197 

9.94858 

9.71339 

10.28661 

10.05142 

10.33803 

40 

21 

66221 

94852 

71370 

28630 

05148 

33779 

39 

22 

66246 

94845 

71401 

28599 

05155 

33754 

38 

23 

66270 

94839 

71431 

28569 

05161 

33730 

37 

24 

66295 

94832 

71462 

28538 

05168 

33705 

36 

25 

66319 

94826 

71493 

28507 

05174 

33681 

35 

26 

66343 

94819 

71524 

28476 

05181 

33657 

34 

27 

66368 

94813 

71555 

28445 

05187 

33632 

33 

28 

66392 

94806 

71586 

28414 

05194 

33608 

32 

29 

66416 

94799 

71617 

28383 

05201 

33584 

31 

30 

9.66441 

9.04793 

9.71648 

10.28352 

10.05207 

10.33559 

30 

31 

66465 

94786 

71679 

28321 

05214 

33535 

29 

32 

'66489 

94780 

71709 

28291 

05220 

33511 

28 

33 

66513 

94773 

71740 

28260 

05227 

33487 

27 

34 

66537 

94767 

71771 

28229 

05233 

33463 

26 

35 

66562 

94760 

71802 

28198 

05240 

33438 

25 

36 

66586 

94753 

71833 

28167 

05247 

33414 

24 

37 

66610 

94747 

71863 

28137 

05253 

33390 

23 

38 

66634 

94740 

71894 

28106 

05260 

33366 

22 

39 

66658 

94734 

71925 

28075 

05266 

33342 

21 

40 

9.66682 

9.94727 

9.71955 

10.28045 

10.05273 

10.33318 

20 

41 

66706 

94720 

71986 

28014 

05280 

33294 

19 

42 

66731 

94714 

72017 

27983 

05286 

33269 

18 

43 

66755 

94707 

72048 

27952 

05293 

33245 

17 

44 

66779 

94700 

72078 

27922 

05300 

33221 

16 

45 

66803 

94694 

72109 

27891 

05306 

33197 

15 

46 

66827 

94687 

72140 

27860 

05313 

33173 

14 

47 

66851 

94680 

72170 

27830 

05320 

33149 

13 

48 

66875 

94674 

72201 

27799 

05326 

33125 

12 

49 

66899 

94667 

72231 

27769 

05333 

33101 

11 

50 

9.66922 

9.94660 

9.72262 

10 27738 

10.05340 

10.33078 

10 

51 

66946 

94654 

72293 

27707 

05346 

33054 

9 

52 

66970 

94647 

72323 

27677 

05353 

33030 

8 

53 

66994 

94640 

72354 

27646 

05360 

33006 

7 

54 

67018 

94634 

72384 

27616 

05366 

32982 

6 

55 

67042 

94627 

72415 

27585 

05373 

32958 

5 

56 

67066 

94620 

72445 

27555 

05380 

32934 

4 

57 

67090 

94614 

72476 

27524 

05386 

32910 

3 

58 

67113 

94607 

72506 

27494 

05393 

32887 

2 

59 

67137 

94600 

72537 

27463 

05400 

32863 

1 

60 

67161 

94593 

72567 

27433 

05407 

32839 

0 


Co-sine. 

Sine. 

Co-tang. 

Tangent. 

Co-secant 

Secant. 

M. 


62 Degrees. 






































































































136 Artificial Sines, Tang, and Sec. 28 Degrees. 


M. 

Sine. 

Co-sine. 

Tangent. 

Co-tang. 

Secant. 

Co-secant 


0 

9.67161 

9.94593 

9.72567 

10.27433 

10.05407 

10.32839 

60 

1 

67185 

94587 

72598 

27402 

05413 

32815 

59 

2 

67208 

94580 

72628 

27372 

05420 

32792 

58 

3 

67232 

94573 

72659 

27341 

05427 

32768 

57 

4 

67256 

94567 

72689 

27311 

05433 

32744 

56 

5 

67280 

94560 

72720 

27280 

05440 

32720 

55 

6 

67303 

94553 

72750 

27250 

05447 

32697 

54 

7 

67327 

94546 

72780 

27220 

05454 

32673 

53 

8 

67350 

94540 

72811 

27189 

05460 

32650 

52 

9 

67374 

94533 

72841 

27159 

05467 

32626 

51 

10 

9.67398 

9.94526 

9.72872 

10.27128 

10.05474 

10.32602 

50 

11 

67421 

94519 

72902 

27098 

05481 

32579 

49 

12 

67445 

94513 

72932 

27068 

05487 

32555 

48 

13 

67468 

94506 

72963 

27037 

05494 

32532 

47 

14 

67492 

94499 

72993 

27007 

05501 

32508 

46 

15 

67515 

94492 

73023 

26977 

05508 

32485 

45 

16 

67539 

94485 

73054 

26946 

05515 

32461 

44 

17 

67562 

94479 

73084 

26916 

05521 

32438 

43 

18 

67586 

94472 

73114 

26886 

05528 

32414 1 

42 

19 

67609 

94465 

73144 

26856 

05535 

32391 

41 

20 

9.67633 

9.94458 

9.73175 

10.26825 

10.05542 

10.32367 

40 

21 

67656 

94451 

73205 

26795 

05549 

32344 

39 

22 

67680 

94445 

73235 

26765 

05555 

32320 

38 

23 

67703 

94438 

73265 

26735 

05562 

32297 

37 

24 

67726 

94431 

73295 

26705 

05569 

32274 

36 

25 

67750 

94424 

73326 

26674 

05576 

32250 

35 

26 

67773 

94417 

73356 

26644 

05583 

32227 

34 

27 

67796 

94410 

73386 

26614 

05590 

32204 

33 

28 

67820 

94404 

73416 

26584 

05596 

32180 

32 

29 

67843 

94397 

73446 

26554 

05603 

32157 

31 

30 

9.67866 

9.94390 

9.73476 

10.26524 

10.05610 

10.32134 

30 

31 

67890 

94383 

73507 

26493 

05617 

32110 

29 

32 

67913 

94376 

73537 

26463 

05624 

32087 

28 

33 

67936 

94369 

73567 

26433 

05631 

32064 

27 

34 

67959 

94362 

73597 

26403 

05638 

32041 

26 

35 

67982 

94355 

73627 

26373 

05645 

32018 

25 

36 

68006 

94349 

73657 

26343 

05651 

31994 

24 

37 

68029 

94342 

73687 

26313 

05658 

31971 

23 

38 

68052 

94335 

73717 

26283 

05665 

31948 

22 

39 

68075 

94328 

73747 

26253 

05672 

31925 

21 

40 

9.68098 

9.94321 

9.73777 

10.26223 

10.05679 

10.31902 

20 

41 

68121 

94314 

73807 

26193 

05686 

31379 

19 

42 

68144 

94307 

73837 

26163 

05693 

31856 

18 

43 

68167 

94300 

73867 

26133 

05700 

31833 

17 

44 

68190 

94293 

73897 

26103 

05707 

31810 

16 

45 

68213 

94286 

73927 

26073 

05714 

31787 

15 

46 

68237 

94279 

73957 

26043 

05721 

31763 

14 

47 

68260 

94273 

73987 

26013 

05727 

31740 

13 

48 

68283 

94266 

74017 

25983 

05734 

31717 

12 

49 

68305 

94259 

74047 

25953 

05741 

31695 

11 

50 

9.68328 

9.94252 

9.74077 

10.25923 

10.05748 

10.31672 

10 

51 

68351 

94245 

74107 

25893 

05755 

31649 

9 

52 

68374 

94238 

74137 

25863 

05762 

31626 

8 

53 

68397 

94231 

74166 

25834 

05769 

31603 

7 

54 

68420 

94224 

74196 

25804 

05776 

31580 

6 

55 

68443 

94217 

74226 

25774 

05783 

31557 

5 

56 

68466 

94210 

74256 

25744 

05790 

31534 

4 

57 

68489 

94203 

74286 

25714 

05797 

31511 

3 

58 

68512 

94196 

74316 

25684 

05804 

31488 

2 

59 

68534 

94189 

74345 

25655 

05811 

31466 

1 

60 

68557 

94182 

74375 

25625 

05818 

31443 

0 


Co-sine. 

Sine. 

Co-tang. 

Tangent. 

Co-secant 

Secant. 

M. 




61 Decrees. 




















































































Artificial Sines, Tang, and Sec. 29 Degrees. 137 


M. 

Sine. 

Co-fine. 

Tangent. 

Co-tang. 

Secant, j 

Co-secant 


0 

9.68557 

9.94182 

9.74375 

10.25625 

10.05818 

10.31443 

60 

1 

68580 

94175 

74405 

25595 

„ 05825 

31420 

59 

2 

68603 

94168 

74435 

25565 

05832 

31397 

58 

3 

68625 

94161 

74465 

25535 

05839 

31375 

57 

4 

68648 

94154 

74494 

25506 

05846 

31352 

56 

5 

68671 

94147 

74524 

25476 

05853 

31329 

55 

6 

68694 

94140 

74554 

25446 

05860 

31306 

54 

7 

68716 

94133 

74583 

25417 

05867 

31284 

53 

8 

68739 

94126 

74613 

. 25387 

05874 

31261 

52 

9 

68762 

94119 

74643 

25357 

05881 

31238 

51 

10 

9.68784 

9.94112 

9.74673 

10.25327 

10.05888 

10.31216 

50 

11 

68807 

94105 

74702 

25298 

05895 

31193 

49 

12 

68829 

94098 

74732 

25268 

05902 

31171 

48 

13 

68852 

94090 

74762 

25238 

05910 

31148 

47 

14 

68875 

94083 

74791 

25209 

05917 

31125 

46 

15 

68897 

94076 

74821 

25179 

05924 

31103 

45 

16 

68920 

94069 

74851 

25149 

05931 

31080 

44 

17 

68942 

94062 

74880 

25120 

05938 

31058 

43 

18 

68965 

94055 

74910 

25090 

05945 

31035 

42 

19 

68987 

94048 

74939 

25061 

05952 

31013 

41 

20 

9.69010 

9.94041 

9.74969 

10.25031 

10.05959 

10.30990 

40 

21 

69032 

94034 

74998 

25002 

05966 

30968 

39 

22 

69055 

94027 

75028 

24972 

05973 

30945 

38 

23 

69077 

94020 

75058 

24942 

05980 

30923 

37 

24 

69100 

94012 

75087 

24913 

05988 

30900 

36 

25 

69122 

94005 

75117 

24883 

05995 

30878 

35 

26 

69144 

93998 

75146 

24854 

06002 

30856 

34 

27 

69167 

93991 

75176 

24824 

06009 

30833 

33 

28 

69189 

93984 

75205 

24795 

06016 

30811 

32 

29 

69212 

93977 

75235 

24765 

06023 

30788 

31 

30 

9.69234 

9.93970 

9.75264 

10.24736 

10.06030 

10.30766 

30 

31 

69256 

93963 

75294 

24706 

06037 

30744 

29 

32 

69279 

93955 

75323 

24677 

06045 

30721 

28 

33 

69301 

93948 

75353 

24647 

06052 

30699 

27 

34 

69323 

93941 

75382 

24618 

06059 

30677 

26 

35 

69345 

93934 

75411 

24589 

06066 

30655 

25 

36 

69368 

93927 

75441 

24559 

06073 

30632 

24 

37 

69390 

93920 

75470 

24530 

06080 

30610 

23 

38 

69412 

93912 

75500 

24500 

06088 

30588 

22 

39 

69434 

93905 

75529 

24471 

06095 

30566 

21 

40 

9.69456 

9.93898 

9.75558 

10.24442 

10.06102 

10.30544 

20 

41 

69479 

93891 

75588 

24412 

06109 

30521 

19 

42 

69501 

93884 

75617 

24383 

06116 

30499 

18 

43 

69523 

93876 

75647 

24353 

06124 

30477 

17 

44 

69545 

93869 

75676 

24324 

06131 

30455 

16 

45 

69567 

93862 

75705 

24295 

06138 

30433 

15 

46 

69589 

93855 

75735 

24265 

06145 

30411 

14 

47 

69611 

93847 

75764 

24236 

06153 

30389 

13 

48 

69633 

93840 

75793 

24207 

06160 

30367 

12 

49 

69655 

93833 

75822 

24178 

06167 

30345 

11 

50 

9.69677 

9.93826 

9.75852 

10.24148 

10.06174 

10.30323 

10 

51 

69699 

93819 

75881 

24119 

06181 

30301 

9 

52 

69721 

93811 

75910 

24090 

06189 

30279 

8 

53 

69743 

93804 

75939 

24061 

06196 

30257 

7 

54 

697(35 

93797 

75969 

24031 

06203 

30235 

6 

55 

69787 

93789 

75998 

24002 

06211 

30213 

5 

56 

69809 

93782 

76027 

23973 

06218 

30191 

4 

57 

69831 

93775 

76056 

23944 

06225 

30169 

3 

58 

69853 

93768 

76086 

23914 

06232 

30147 

2 

59 

69875 

93760 

76115 

23885 

06240 

30125 

1 

60 

69897 

93753 

76144 

23856 

06247 

30103 

0 


i Co-fine. 

Sine. 

Co-tang. 

I Tangent. 

Co-secant 

I Secant. 

M. 


b 60 Degrees. 
















































































138 Artificial Sines, Tang, and Sec. 30 Degrees. 


M. 

Sine. 

Co-sine. 

Tangent. 

Co-tang. 

Secant. 

Co-secant 


0 

9.69897 

9.93753 

9.76144 

10.23856 

10.06247 

10.30103 

60 

1 

69919 

93746 

76173 

23827 

06254 

30081 

59 

2 

69941 

93738 

76202 

23798 

06262 

30059 

58 

3 

69963 

93731 

76231 

23769 

06269 

30037 

57 

4 

69984 

93724 

76261 

23739 

06276 

30016 

56 

5 

70006 

93717 

76290 

23710 

06283 

29994 

55 

6 

70028 

93709 

76319 

23681 

06291 

29972 

54 

7 

70050 

93702 

76348 

23652 

06298 

29950 

53 

8 

70072 

93695 

76377 

23623 

06305 

29928 

52 

9 

70093 

93687 

76406 

23594 

06313 

29907 

51 

10 

9.70115 

9.93630 

9.76435 

10.23565 

10.06320 

10.29885 

50 

11 

70137 

93673 

76464 

23536 

06327 

29863 

49 

12 

70159 

93665 

76493 

23507 

06335 

29841 

48 

13 

70180 

93658 

76522 

23478 

06342 

29820 

47 

14 

70202 

93650 

76551 

23449 

06350 

29798 

46 

15 

70224 

93643 

76580 

23420 

06357 

29776 

45 

16 

70245 

93636 

76609 

23391 

06364 

29755 

44 

17 

70267 

93628 

76639 

23361 

06372 

29733 

43 

18 

70288 

93621 

76668 

23332 

06379 

29712 

42 

19 

70310 

93614 

76697 

23303 

06386 

29690 

41 

20 

9.70332 

9.93606 

9.76725 

10.23275 

10.06394 

10.29668 

40 

21 

70353 

93599 

76754 

23246 

06401 

29647 

39 

22 

70375 

93591 

76783 

23217 

06409 

29625 

38 

23 

70396 

93584 

76812 

23188 

06416 

29604 

37 

24 

70418 

93577 

76841 

23159 

06423 

29582 

36 

25 

70439 

93569 

76870 

23130 

06431 

29561 

35 

26 

70461 

93562 

76899 

23101 

06438 

29539 

34 

27 

70482 

93554 

76928 

23072 

06446 

29518 

33 

28 

70504 

93547 

76957 

23043 

06453 

29496 

32 

29 

70525 

93539 

76986 

23014 

06461 

29475 

31 

30 

9.70547 

9.93532 

9.77015 

10.22985 

10.06468 

10.29453 

30 

31 

70568 

93525 

77044 

22956 

06475 

29432 

29 

32 

70590 

93517 

77073 

22927 

06483 

29410 

28 

33 

70611 

93510 

77101 

22899 

06490 

29389 

27 

34 

70633 

93502 

77130 

22870 

06498 

29367 

26 

35 

70654 

93495 

77159 

22841 

06505 

29346 

25 

36 

70675 

93487 

77188 

22812 

06513 

29325 

24 

37 

70697 

93480 

77217 

22783 

06520 

29303 

23 

38 

70718 

93472 

77246 

22754 

06528 

29282 

22 

39 

70739 

93465 

77274 

22726 

06535 

29261 

21 

40 

9.70761 

9.93457 

9.77303 

10.22697 

10.06543 

10.29239 

20 

41 

70782 

93450 

77332 

22668 

06550 

29218 

19 

42 

70803 

93442 

77361 

22639 

06558 

29197 

18 

43 

70824 

93435 

77390 

22610 

06565 

29176 

17 

44 

70846 

93427 

77418 

22582 

06573 

29154 

16 

45 

70867 

93420 

77447 

22553 

06580 

29133 

15 

46 

70888 

93412 

77476 

22524 

06588 

29112 

14 

47 

70909 

93405 

77505 

22495 

06595 

29091 

13 

48 

70931 

93397 

77533 

22467 

06603 

29069 

12 

49 

70952 

93390 

77562 

22438 

06610 

29048 

11 

50 

9.70973 

9.93382 

9.77591 

10.22409 

10.06618 

10.29027 

10 

51 

70994 

93375 

77619 

22381 

06625 

29006 

9 

52 

71015 

93367 

77648 

22352 

06633 

28985 

8 

53 

71036. 

r 93360 

77677 

22323 

06640 

28964 

7 

54 

71058 

93352 

77706 

22294 

06648 

28942 

6. 

55 

71079 

93344 

77734 

22266 

06656 

28921 

5 

56 

71100 

93337 

77763 

22237 

06663 

28900 

4 

57 

71121 

93329 

77791 

22209 

06671 

28879 

3 

58 

71142 

93322 

77820 

22180 

06678 

28858 

2 

59 

71163 

93314 

77849 

22151 

06686 

28837 

1 

60 

71184 

93307 

77877 

22123 

06693 

28816 

0 

—— 

Co-sine. 

Sine. 

Co-tang. 

Tangent. 

Co-secant 

Secant. 

M. 


59 Degrees 







































































Artificial Sines, Tang, and Sec. 31 Degrees. 139 


M. 

Sine. 

Co-sine. 

Tangent. 

Co-tang. 

Secant. 

Co-secant 


0 

9.71184 

9.93307 

9.77877 

10.22123 

10.06693 

10.28816 

60 

1 

71205 

93299 

77906 

22094 

06701 

28795 

59 

2 

71226 

93291 

77935 

22065 

06709 

28774 

58 

3 

71247 

93284 

77963 

22037 

06716 

28753 

57 

4 

71268 

93276 

77992 

22008 

06724 

28732 

56 

5 

71289 

93269 

78020 

21980 

06731 

28711 

55 

6 

71310 

93261 

78049 

21951 

06739 

28690 

54 

7 

71331 

93253 

78077 

21923 

06747 

28669 

53 

8 

71352 

93246 

78106 

21894 

06754 

28648 

52 

9 

71373 

93238 

78135 

21865 

06762 

28627 

51 

10 

9.71393 

9.93230 

9.78163 

10.21837 

10.06770 

10.28607 

50 

11 

71414 

93223 

78192 

21808 

06777 

28586 

49 

12 

71435 

93215 

78220 

21780 

06785 

28565 

48 

13 

71456 

93207 

78249 

21751 

06793 

28544 

47 

14 

71477 

93200 

78277 

21^23 

06800 

28523 

46 

15 

71498 

93192 

78306 

21694 

06808 

28502 

45 

16 

71519 

93184 

78334 

21666 

06816 

28481 

44 

17 

71539 

93177 

78363 

21637 

06823 

28461 

43 

18 

71560 

93169 

78391 

21609 

06831 

28440 

42 

19 

71581 

93161 

78419 

21581 

06839 

28419 

41 

20 

9.71602 

9.93154 

9.78448 

10.21552 

10.06846 

10.28398 

40 1 

21 

71622 

93146 

78476 

21524 

06854 

28378 

39 

22 

71643 

93138 

78505 

21495 

* 06862 

28357 

38 

23 

71664 

93131 

78533 

21467 

06869 

28336 

37 

24 

71685 

93123 

78562 

21438 

06877 

28315 

36 

25 

71705 

93115 

78590 

21410 

06885 

28295 

35 

26 

71726 

93108 

78618 

21382 

06892 

28274 

34 

27 

71747 

93100 

78647 

21353 

06900 

28253 

33 

28 

71767 

93092 

78675 

21325 

06908 

28233 

32 

29 

71788 

93084 

78704 

21296 

06916 

28212 

31 

30 

9.71809 

9.93077 

9.78732 

10.21268 

10.06923 

10.28191 

30 

31 

71829 

93069 

78760 

21240 

06931 

28171 

29 

32 

71850 

93061 

78789 

21211 

06939 

28150 

28 

33 

71870 

93053 

78817 

21183 

06947 

28130 

27 

34 

71891 

93046 

78845 

21155 

06954 

28109 

26 , 

35 

71911 

93038 

78874 

21126 

06962 

28089 

25 

36 

71932 

93030 

78902 

21098 

06970 

28068 

24 

37 

71952 

93022 

78930 

21070 

06978 

. 28048 

23 

38 

71973 

93014 

78959 

21041 

06986 

28027 

22 

39 

71994 

93007 

78987 

21013 

06993 

28006 

21 

40 

9.72014 

9.92999 

9.79015 

10.20985 

10.07001 

10.27986 

20 

41 

72034 

92991 

79043 

20957 

07009 

27966 

19 

42 

72055 

92983 

79072 

20928 

07017 

27945 

18 

43 

72075 

92976 

79100 

20900 

07024 

27925 

17 

44 

72096 

92968 

79128 

20872 

07032 

27904 

16 

45 

72116 

92960 

79156 

20844 

07040 

27884 

15 

46 

72137 

92952 

79185 

20815 

07048 

27863 

14 

47 

72157 

92944 

79213 

20787 

07056 

27843 

13 

48 

72177 

92936 

7924 J 

20759 

07064 

27823 

12 

49 

72198 

92929 

79269 

20731 

07071 

27802 

11 j 

50 

9.72218 

9.92921 

9.79297 

10.20703 

10.07079 

10.27782 

10 

51 

72238 

92913 

79326 

20674 

07087 

27762 

9 

52 

72259 

92905 

79354 

20646 

07095 

27741 

8 

53 

72279 

92897 

79382 

20618 

07103 

27721 

7 

54 

72299 

92889 

79410 

20590 

07111 

27701 

6 I 

55 

72320 

92881 

79438 

20562 

07119 

27680 

5 

56 

72340 

92874 

79466 

20534 

07126 

27660 

4 

57 

72360 

92866 

79495 

20505 

07134 

27640 

3 

58 

72381 

92858 

79523 

20477 

07142 

27619 

2 1 

59 

72401 

92850 

79551 

20449 

07150 

27599 

1 1 

60 

72421 

92842 

79579 

20421 

07158 

27579 

0 


Co-pine. 

Sine. 

Co-tang. 

Tangent. 

Co-secant. 

Secant. 

M. J 


53 Degrees, 




















































































140 Artificial Sines, Tang, and Sec. 32 Degrees. 


M. 

Sine. 

Co-sine. 

Tangent. 

Co-tang. 

Secant. 

Co-secant 


0 

9.72421 

9.92842 

9.79579 

10.20421 

10.07158 

10.27579 

60 

1 

72441 

92834 

79607 

20393 

07166 

27559 

59 

2 

72461 

92826 

79635 

20365 

07174 

27539 

58 

3 

72482 

92818 

79663 

20337 

07182 

27518 

57 

4 

72502 

92810 

79691 

20309 

07190 

27498 

56 

5 

72522 

92803 

79719 

20281 

07197 

27478 

55 

6 

72542 

92795 

79747 

20253 

07205 

27458 

54 

7 

72562 

92787 

79776 

20224 

07213 

27438 

53 

8 

72582. 

92779 

79804 

20196 

07221 

27418 

52 

9 

72602 

92771 

79832 

20168 

07229 

27398 

51 

10 

9.72622 

9.92763 

9.79860 

10.20140 

10.07237 

10.27378 

50 

11 

72643 

92755 

79888 

20112 

07245 

27357 

49 

12 

72663 

92747 

79916 

20084 

07253 

27337 

48 

13 

72683 

92739 

79944 

20056 

07261 

27317 

47 

14 

72703 

92731 

79972 

20028 

07269 

27297 

46 

15 

72723 

92723 

80000 

20000 

07277 

27277 

45 

16 

72743 

92715 

80028 

19972 

07285 

27257 

44 

17 

72763 

92707 

80056 

19944 

07293 

27237 

43 

18 

72783 

92699 

80084 

19916 

07301 

27217 

42 

19 

72803 

92691 

80112 

19888 

07309 

27197 

41 

20 

9.72823 

9.92683 

9.80140 

10.19860 

10.07317 

1(> 27177 

40 

21 

72843 

92675 

80168 

19832 

07325 

27157 

39 

22 

72863 

92667 

80195 

19805 

07333 

27137 

38 

23 

72883 

92659 

80223 

19777 

07341 

27117 

37 

24 

72902 

92651 

80251 

19749 

07349 

27098 

36 

25 

72922 

92643 

80279 

19721 

07357 

27078 

35 

26 

72942 

92635 

80307 

19693 

07365 

27058 

34 

27 

72962 

92627 

80335 

19665 

07373 

27038 

33 

28 

72982 

92619 

80363 

19637 

07381 

27018 

32 

29 

73002 

92611 

80391 

19609 

07389 

26998 

31 

30 

9.73022 

9.92603 

9.80419 

10.19581 

10.07397 

10.26978 

30 

31 

73041 

92595 

80447 

19553 

07405 

26959 

29 

32 

73061 

92587 

80474 

19526 

07413 

26939 

28 

33 

73081 

92579 

80502 

19498 

07421 

26919 

27 

34 

73101 

92571 

80530 

19470 

07429 

26899 

26 

35 

73121 

92563 

80558 

19442 

07437 

26879 

25 

36 

73140 

92555 

80586 

19414 

07445 

26860 

24 

37 

73160 

92546 

80614 

19386 

07454 

26840 

23 

38 

73180 

92538 

80642 

19358 

07462 

26820 

22 

39 

73200 

92530 

80669 

19331 

07470 

26800 

21 

40 

9.73219 

9.92522 

9.80697 

10.19303 

10.07478 

10.26781 

20 

41 

73239 

92514 

80725 

19275 

07486 

26761 

19 

42 

73259 

92506 

80753 

19247 

07494 

26741 

18 

43 

73278 

92498 

80781 

19219 

07502 

26722 

17 

44 

73298 

92490 

80808 

19192 

07510 

26702 

16 

45 

73318 

92482 

80836 

19164 

07518 

26682 

15 

46 

73337 

92473 

80864 

19136 

07527 

26663 

14 

47 

73357 

92465 

80892 

19108 

07535 

26643 

13 

43 

73377 

92457 

80919 

19081 

07543 

26623 

12 

49 

73396 

92449 

80947 

19053 

07551 

26604 

11 

50 

9.73416 

9.92441 

9.80975 

10.19025 

10.07559 

10.26584 

10 

51 

73435 

92433 

81003 

18997 

07567 

26565 

9 

52 

73455 

92425 

81030 

18970 

07575 

26545 

8 

53 

73474 

92416 

81058 

18942 

07584 

26526 

7 

54 

73494 

92408 

81086 

18914 

07592 

26506 

6 

1 55 

73513 

92400 

81113 

18887 

07600 

26487 

5 

56 

73533 

92392 

81141 

18859 

07608 

26467 

4 

57 

73552 

92384 

81169 

18831 

07616 

26448 

3 

58 

73572 

92376 

81196 

18804 

07624 

26428 

2 

59 

73591 

92367 

81224 

18776 

07633 

26409 

1 

60 

73611 

92359 

81252 

18748 

07641 

26389 

0 


Co-sine. 

Sine. 

Co-tang. 

Tangent. 

Co-secant 

Secant. 

M. 


57 Degrees 


















































































Artificial Sines, Tang, and Sec. 33 Degrees. 141 


M. 

Sine. 

Co-sine. | 

Tangent. 1 

Co-tang. 

Secant. 

Co-secant 

j 

0 

9.73611 

9.92359 

9.81252 

10.18748 

10.07641 

10.26389 

60 il 

1 

73630 

92351 

81279 

18721 

07649 

26370 

59 V 

2 

73650 

92343 

81307 

18693 

07657 

26350 

58 

3 

73669 

92335 

81335 

18665 

07665 

26331 

57 I 

4 

73689 

92326 

81362 

18638 

07674 

26311 

56 

5 

73708 

92318 

81390 

18610 

07682 

26292 

55 I 

6 

73727 

92310 

81418 

18582 

07690 

26273 

54 

7 

73747 

92302 

81445 

18555 

07698 

26253 

53 1 

8 

73766 

92293 

81473 

18527 

07707 

26234 

52 

9 

73785 

92285 

81500 

18500 

07715 

26215 

51 1 

10 

9.73805 

9.92277 

9.81528 

10.18472 

10.07723 

10.26195 

50 1 

11 

73824 

. 92269 

81556 

18444 

07731 

26176 

49 1 

12 

73843 

92260 

81583 

18417 

07740 

26157 

48 1 

13 

73863 

92^52 

81611 

18389 

07748 

26137 

47 1 

14 

73882 

92244 

81638 

18362 

07756 

26118 

46 I 

15 

73901 

92235 

81666 

18334 

07765 

26099 

45 

16 

73921 

92227 

81693 

18307 

07773 

26079 

44 

17 

73940 

92219 

81721 

18279 

07781 

26060 

43 1 

18 

73959 

92211 

81748 

18252 

07789 

26041 

42 1 

19 

73978 

92202 

81776 

18224 

07798 

26022 

41 I 

20 

9.73997 

9.92194 

9.81803 

10.18197 

10.07806 

10.26003 

40 1 

21 

74017 

92186 

81831 

18169 

07814 

25983 

39 I 

22 

74036 

92177 

81858 

18142 

07823 

25964 

38 || 

23 

74055 

92169 

81886 

18114 

07831 

25945 

37 || 

24 

74074 

92161 

81913 

18087 

07839 

25926 

36 1 

25 

74093 

92152 

81941 

18059 

07848 

25907 

35 

26 

74113 

92144 

81968 

18032 

07856 

25887 

34 1 

27 

74132 

92136 

81996 

18004 

07864 

25868 

33 1 

28 

74151 

92127 

82023 

17977 

07873 

25849 

32 [3 

29 

74170 

92119 

82051 

17949 

07881 

25830 

31 I 

30 

9.74189 

9.92111 

9.82078 

10.17922 

10.07889. 

10.25811 

30 11 

31 

74208 

92102 

82106 

17894 

07898 

25792 

29 I 

32 

74227 

92094 

82133 

17867 

07906 

25773 

28 1 

33 

74246 

92086 

82161 

17839 

07914 

25754 

27 J 

34 

74265 

92077 

82188 

17812 

07923 

25735 

26 I 

35 

74284 

92069 

82215 

17785 

07931 

25716 

25 1 

36 

74303 

92060 

82243 

17757 

07940 

25697 

24 1 

37 

74322 

92052 

82270 

17730 

07948 

25678 

23 y 

38 

74341 

92044 

82298 

17702 

07956 

25659 

22 1 

39 

74360 

92035 

82325 

17675 

07965 

25640 

21 J 

40 

9.74379 

9.92027 

9.82352 

10.17648 

10.07973 

10.25621 

20 

41 

74398 

92018 

82380 

17620 

07982 

25602 

19 I 

42 

74417 

92010 

82407 

17593 

07990 

25583 

18 1 

43 

74436 

92002 

82435 

17565 

07998 

25564 

17 1 

44 

74455 

91993 

82462 

17538 

08007 

25545 

16 || 

45 

74474 

91985 

82489 

17511 

08015 

25526 

15 

46 

74493 

91976 

82517 

17483 

08024 

25507 

14 | 

47 

74512 

91968 

82544 

17456 

08032 

25488 

13 

48 

74531 

91959 

82571 

17429 

08041 

25469 

12 I 

49 

74549 

91951 

82599 

17401 

08049 

25451 

11 1 

50 

9.74568 

9.91942 

9.82626 

10.17374 

10.08058 

10.25432 

lOj 

51 

74587 

91934 

82653 

17347 

08066 

25413 

9 jl 

52 

74606 

91925 

82681 

17319 

08075 

25394 

8 

53 

74625 

91917 

82708 

17292 

08083 

25375 

71 

54 

74644 

91908 

82735 

17265 

08092 

25356 

6 1 

55 

74662 

91900 

82762 

17238 

08100 

25338 

5 | 

56 

74681 

91891 

82790 

17210 

08109 

25319 

4 j 

57 

74700 

91883 

82817 

17183 

08117 

25300 

I 

58 

74719 

91874 

82844 

17156 

08126 

25281 

2 l| 

59 

74737 

91866 

82871 

17129 

08134 

25263 


60 

74756 

91857 

,82899 

17101 

08143 

25244 

U 1 


Co-sine. 

Sine. 

Co-tang. 

Tangent. 

Co-secant 

Serant. 

M. 1 


56 Degrees. 






















































































142 Artificial Sines, Tang, and Sec. 34 Degrees. 


M. 

Sine. 

Co-sine. 

Tangent. 

Co-tang. 

Secant. 

Co-secant 


0 

9.74756 

9.91857 

9.82899 

10.17101 

10.08143 

10.25244 

60 

1 

74775 

91849 

82926 

17074 

08151 

25225 

59 

2 

74794 

91840 

82953 

17047 

08160 

25206 

58 

l 3 

74812 

91832 

82980 

17020 

08168 

- 25188 

57 

4 

74831 

91823 

83008 

16992 

08177 

25169 

56 

5 

74850 

91815 

83035 

16965 

08185 

25150 

55 

6 

• 74868 

91806 

83062 

16938 

08194 

25132 

54 

7 

74887 

91798 

83089 

16911 

08202 

25113 

53 

8 

74906 

91789 

83117 

16883 

08211 

25094 

52 

9 

74924 

91781 

83144 

16856 

08219 

25076 

51 

10 

9.74943 

9.91772 

9.83171 

10.16829 

10.08228 

10.25057 

50 

11 

74961 

91763 

83198 

16802 

08237 

25039 

49 

12 

74980 

91755 

83225 

16775 

08245 

**5020 

48 ! 

13 

74999 

91746 

83252 

16748 

08254 

25001 

47 

14 

75017 

91738 

83280 

16720 

08262 

24983 

46 

15 

75036 

91729 

83307 

16693 

08271 

24964 

45 

16 

75054 

91720 

83334 

16666 

08280 

24946 

44 

17 

75073 

91712 

83361 

16639 

08288 

24927 

43 

18 

75091 

91703 

83388 

16612 

08297 

24909 

42 

19 

75110 

91695 

83415 

16585 

08305 

24890 

41 

20 

9.75128 

9.91686 

9.83442 

10.16558 

10.08314 

10.24872 

40 

21 

75147 

91677 

83470 

16530 

08323 

24853 

39 

22 

75165 

91669 

83497 

16503 

08331 

24835 

38 

23 

75184 

91660 

83524 

16476 

08340 

24816 

37 

24 

75202 

91651 

83551 

16449 

08349 

24798 

36 

25 

75221 

91643 

83578 

16422 

08357 

24779 

35 

; 26 

75239 

91634 

83605 

16395 

08366 

24761 

34 

27 

75258 

91625 

83632 

16368 

08375 

24742 

33 

28 

75276 

91617 

83659 

16341 

08383 

24724 

32 

29 

75294 

91603 

83686 

16314 

08392 

24706 

31 

30 

9.75313 

9.91599 

9.83713 

10.16287 

10.08401 

10.24687 

30 

31 

75331 

91591 

83740 

16260 

08409 

24669 

29 

32 

75350 

91582 

83768 

16232 

08418 

24650 

28 

33 

75368 

91573 

83795 

16205 

08427 

24632 

27 

34 

75386 

91565 

83822 

16178 

08435 

24614 

26 

35 

75405 

91556 

83849 

16151 

08444 

24595 

25 

36 

, 75423 

91547 

83876 

16124 

08453 

24577 

24 

37 

75441 

91533 

83903 

‘16097 

08462 

24559 

23 

38 

75459 

91530 

83930 

16070 

08470 

24541 

22 

39 

75478 

91521 

83957 

16043 

08479 

24522 

21 

40 

9.75496 

9.91512 

9.83984 

10.16016 

10.08488 

10.24504 

20 

41 

75514 

91504 

84011 

15989 

08496 

24486 

19 

42 

75533 

91495 

84038 

15962 

08505 

24467 

18 

43 

75551 

91486 

84065 

15935 

08514 

24449 

17 

44 

75569 

91477 

84092 

15908 

08523 

24431 

16 

45 

75587 

91469 

84119 

15881 

08531 

24413 

15 

46 

75605 

91460 

84146 

15854 

08540 

24395 

14 

47 

75624 

91451 

84173 

15827 

08549 

24376 

13 

48 

75642 

91442 

84200 

15800 

08558 

24358 

12 

1 49 

75660 

91433 

84227 

15773 

08567 

24340 

11 

50 

9.75678 

9.91425 

9.84254 

10.15746 

10.08575 

10.24322 

10 

51 

75696 

91416 

84280 

15720 

08584 

24304 

9 

52 

75714 

91407 

84307 

15693 

08593 

24286 

8 

53 

75733 

91398 

84334 

15666 

08602 

24267 

7 

54 

75751 

91389 

84361 

15639 

08611 

24249 

6 

55 

75769 

91381 

84388 

15612 

08619 

24231 

5 

56 

75787 

91372 

84415 

15585 

08628 

24213 

4 

57 

75805 

91363 

84442 

15558 

08637 

24195 

3 

58 

75823 

91354 

84469 

15531 

08646 

24177 

2 

59 

75841 

91345 

84496 

15504 

08655 

24159 

1 

! 60 

75859 

91336 

84523 

15477 

08664 

24141 

0 


Co-sine. 

Sine. 

Co-tang. 

''nngent. 

Co-secant 

Secant. 

M. 


55 Degrees. 















































































Artificial Sines, Tang, and Sec. 35 Degrees. 143 


1V1. 

Sine. 

Co-sine. 

Tangent. 1 

Co-tang. 

Secant. 

Co-secant 


0 

9.75359 

9.91336 

9.84523 

10.15477 

10.08664 

10.24141 

60 

1 

75877 

91328 

84550 

15450 

08672 

24123 

59 

2 

75895 

91319 

84576 

15424 

08681 

24105 

58 

3 

75913 

91310 

84603 

15397 

08690 

24087 

57 

4 

75931 

91301 

84630 

15370 

08699 

24069 

56 

5 

75949 

91292 

84657 

15343 

08708 

24051 

55 

6 

75967 

91283 

84684 

15316 

08717 

24033 

54 

7 

75985 

91274 

84711 

15289 

08726 

24015 

53 

8 

76003 

91266 

84738 

15262 

08734 

23997 

52 

9' 

76021 

91257 

84764 

15236 

08743 

23979 

51 

10 

9.76039 

9.91248 

9.84791 

10.15209 

10.08752 

10.23961 

50 

11 

76057 

91239 

84818 

15182 

08761 

23943 

49 

12 

76075 

91230 

84845 

15155 

08770 

23925 

48 

13 

76093 

91221 

84872 

15128 

08779 

23907 

47 

14 

76111 

91212 

84899 

15101 

08788 

23889 

46 

15 

76129 

91203 

84925 

15075 

08797 

23871 

45 

16 

76146 

91194 

84952 

15048 

08806 

23854 

44 

17 

76164 

91185 

84979 

15021 

08815 

23836 

43 

18 

76182 

91176 

85006 

14994 

08824 

23818 

42 

19 

76200 

91167 

85033 

14967 

08833 

23800 

41 

20 

9.76218 

9.91158 

9.85059 

10.14941 

10.08842 

10.23782 

40 

21 

76236 

91149 

85086 

14914 

08851 

23764 

39 

22 

76253 

91141 

85113 

14887 

08859 

23747 

38 

. 23 

76271 

91132 

85140 

14860 

08868 

23729 

37 

24 

76289 

91123 

85166 

14834 

08877 

23711 

36 

25 

76307 

91114 

85193 

14807 

08886 

23693 

35 

26 

76324 

91105 

85220 

14780 

08895 

23676 

34 

27 

76342 

91096 

85247 

14753 

08904 

23658 

33 

28 

76360 

91087 

85273 

14727 

08913 

23640 

32 

29 

76378 

91078 

85300 

14700 

08922 

23622 

31 

30 

9.76395 

9.91069 

9.85327 

10.14673 

10.08931 

10.23605 

30 

31 

. 76113 

91060 

85354 

14646 

08940 

23587 

29 

32 

76431 

91051 

85380 

14620 

08949 

23569 

28 

33 

76448 

91042 

85407 

14593 

08958 

23552 

27 

34 

76466 

91033 

85434 

14566 

08967 

23534 

26 

35 

76484 

91023 

85460 

14540 

08977 

23516 

25 

36 

76501 

91014 

85487 

14513 

08986 

23499 

24 

37 

76519 

91005 

85514 

14486 

08995 

23481 

23 

38 

76537 

90996 

85540 

14460 

09004 

23463 

22 

39 

76554 

90987 

85567 

14433 

09013 

23446 

21 

40 

9.76572 

9.90978 

9.85594 

10.14406 

10.09022 

10.23428 

20 

41 

76590 

90969 

85620 

14380 

09031 

23410 

19 

42 

76607 

90960 

85647 

14353 

09040 

23393 

18 

43 

76625 

90951 

85674 

14326 

09049 

23375 

17 

44 

76642 

90942 

85700 

14300 

09058 

23358 

16 

45 

76660 

90933 

85727 

14273 

09067 

23340 

15 

46 

76677 

90924 

85754 

14246 

09076 

23323 

14 

47 

76695 

90915 

85780 

14220 

09085 

23305 

13 

48 

76712 

90906 

85807 

14193 

09094 

23288 

12 

49 

76730 

90896 

85834 

14166 

09104 

23270 

11 

50 

9.76747 

9.90887 

9.85860 

10.14140 

10.09113 

10.23253 

10 

51 

76765 

90878 

85887 

14113 

09122 

23235 

9 

52 

76782 

90869 

85913 

14087 

09131 

23218 

8 

53 

76800 

90860 

85940 

14060 

09140 

23200 

7 

54 

76817 

90851 

85967 

14033 

09149 

23183 

6 

55 

76835 

90842 

85993 

14007 

09158 

23165 

5 

56 

76852 

90832 

86020 

13980 

09168 

23148 

4 

57 

76870 

90823 

86046 

13954 

09177 

23130 

3 

58 

76887 

90814 

86073 

13927 

09186 

23113 

2 

59 

76904 

90805 

86100 

13900 

09195 

23096 

1 

60 

76922 

90796 

86126 

13874 

09204 

23078 

0 


Co-sine. 

Sine. 

Co-tang. 

Tangent. 

Co-secant 

decant. 

M. 


54 Degrees. 










































































144 Artificial Sines, Tang, and Sec. 36 Degrees. 


M. 

Sine. 

Co-sine. 

Tangent. 

Co-tang. 

Secant. 

Co-secant 


0 

9.76922 

9.90796 

9.86126 

10.13874 

10.09204 

10.23078 

60 

1 

76939 

90787 

86153 

13847 

09213 

23061 

59 

2 

76957 

90777 

86179 

13821 

09223 

23043 

58 

3 

76974 

90768 

86206 

13794 

09232 

23026 

57 

4 

76991 

90759 

86232 

13768 

09241 

23009 

56 

5 

77009 

90750 

86259 

13741 

09250 

22991 

55 

6 

77026 

90741 

86285 

13715 

09259 

22974 

54 ' 

7 

77043 

90731 

86312 

13688 

09269 

22957 

53 

8 

77061 

90722 

86338 

13662 

09278 

22939 

52 

9 

77078 

90713 

86365 

13635 

09287 

22922 

51 

10 

9.77095 

9.90704 

9.86392 

10.13608 

10.09296 

10.22905 

50 

11 

77112 

. 90694 

86418 

13582 

09306 

22888 

49 

12 

77130 

90685 

86445 

13555 

09315 

22870 

48 

13 

77147 

90676 

86471 

13529 

09324 

22853 

47 

14 

77164 

90667 

86498 

13502 

09333 

22836 

46 

15 

77181 

90657 

86524 

13476 

09343 

22819 

45 

16 

■ ,77199 

90648 

86551 

13449 

09352 

22801 

44 

17 

77216 

90639 

86577 

13423 

09361 

22784 

43 

18 

77233 

90630 

86603 

13397 

09370 

22767 

42 

19 

77250 

90620 

86630 

13370 

09380 

22750 

41 

20 

9.77268 

9.90611 

9.86656 

10.13344 

10.09389 

10.22732 

40 

21 

77285 

90602 

86683 

13317 

09398 

22715 

39 

22 

77302 

90592 

86709 

13291 

09408 

22698 

38 

23 

77319 

90583 

86736 

13264 

09417 

22681 

37 

24 

77336 

90574 

86762 

13238 

09426 

22664 

36 

25 

77353 

90565 

86789 

13211 

09435 

22647 

35 

26 

77370 

90555 

86815 

13185 

09445 

22630 

34 

27 

77387 

90546 

86842 

13158 

09454 

22613 

33 

28 

77405 

90537 

86868 

13132 

09463 

22595 

32 

29 

77422 

90527 

86894 

13106 

09473 

22578 

31 

30 

9.77439 

9.90518 

9.86921 

10.13079 

10.09482 

10.22561 

30 

31 

77456 

90509 

86947 

13053 

09491 

22544 

29 

32 

77473 

90499 

86974 

13026 

09501 

22527 

28 

33 

77490 

90490 

87000 

13000 

09510 

22510 

27 

34 

77507 

90480 

87027 

12973 

09520 

22493 

26 

35 

77524 

90471 

87053 

12947 

09529 

22476 

25 

36 

77541 

90462 

87079 

12921 

09538 

22459 

24 

37 

77558 

90452 

87106 

12894 

09548 

22442 

23 

38 

77575 

90443 

87132 

12868 

09557 

22425 

22 

39 

77592 

90434 

87158 

12842 

09566 

22408 

21 

40 

9.77609 

9.90424 

9.87185 

10.12815 

10.09576 

10.22391 

20 

41 

77626 

90415 

87211 

12789 

09585 

22374 

19 

42 

77643 

90405 

87238 

12762 

09595 

22357 

18 

43 

77660 

90396 

87264 

12736 

09604 

22340 

17 

44 

77677 

90386 

87290 

12710 

09614 

22323 

16 

45 

77694 

90377 

87317 

12683 

09623 

22306 

15 

46 

77711 

90368 

67343 

12657 

09632 

22289 

14 

47 

77728 

90358 

87369 

12631 

09642 

22272 

13 

48 

77744 

90349 

87396 

12604 

09651 

22256 

12 

49 

77761 

90339 

87422 

12578 

09661 

22239 

11 

50 

9.77778 

9.90330 

9.87448 

10.12552 

10.09670 

10.22222 

10 

51 

77795 

90320 

87475 

12525 

09680 

22205 

9 

52 

77812 

90311 

87501 

12499 

09689 

22188 

8 

53 

77829 

90301 

87527 

12473 

09699 

22171 

7 

54 

77846 

90292 

87554 

12446 

09708 

22154 

6 

55 

77862 

90282 

87580 

12420 

09718 

22138 

5 

56 

77879 

90273 

87606 

12394 

09727 

22121 

4 

57 

77896 

90263 

87633 

12367 

09737 

22104 

3 

58 

77913 

90254 

87659 

12341 

09746 

22087 

2 

59 

77930 

90244 

87685 

12315 

09756 

22070 

t 

60 

77946 

90235 

87711 

12289 

09765 

22054 

0 


Co-sine. 

Sine. 

Co-tang. 

Tangent. 

I Co-secant 

Secant. 

M. 


63 Degrees 











































































Artificial Sines, Tang, and Sec. 37 Degrees. 145 


M. 

Sine. 

Co-sine. 

Tangent. 

Co-tang. 

Secant. 

Co-secant 


0 

9.77946 

9.90235 

9.87711 

10.12289 

10.09765 

10.22054 

60 

l 

77963 

90225 

87738 

12262 

09775 

22037 

59 

2 

77980 

90216 

87764 

12236 

09784 

22020 

58 

3 

77997 

90206 

87790 

12210 

09794 

22003 

57 

4 

78013 

90197 

87817 

12183 

' 09803 

21987 

56 

5 

78030 

90187 

87843 

12157 

09813 

21970 

55 

6 

78047 

90178 

87869 

12131 

09822 

21953 

54 

7 

78063 

90168 

87895 

12105 

09832 

21937 

53 

8 

78080 

90159 

87922 

12078 

09841 

21920 

52 

9 

78097 

90149 

87948 

12052 

09851 

21903 

51 

10 

9.78113 

9.90139 

9.87974 

10.12026 

10.09861 

10.21887 

50 

11 

78130 

90130 

88000 

12000 

09870 

21870 

49 

12 

78147 

90120 

88027 

11973 

09880 

21853 

48 

13 

78163 

90111 

88053 

11947 

09889 

21837 

47 

14 

78180 

90101 

88079 

11921 

09899 

21820 

46 

15 

78197 

90091 

88105 

11895 

09909 

21803 

45 

16 

78213 

90082 

88131 

11869 

09918 

21787 

44 

17 

78230 

90072 

88158 

11842 

09928 

21770 

43 

18 

78246 

90063 

88184 

11816 

09937 

21754 

42 

19 

78263 

90053 

88210 

11790 

09947 

21737 

41 

20 

9.78280 

9.90043 

9.88236 

10.11764 

10.09957 

10.21720 

40 

21 

78296 

90034 

88262 

11738 

09966 

21704 

39 

22 

78313 

90024 

88289 

11711 

09976 

21687 

38 

23 

78329 

90014 

88315 

11685 

09986 

21671 

37 

24 

78346 

90005 

88341 

11659 

09995 

21654 

36 

25 

78362 

89995 

88367 

11633 

10005 

21638 

35 

26 

78379 

89985 

88393 

11607 

10015 

21621 

34 

27 

78395 

89976 

88420 

11580 

10024 

21605 

33 

28 

78412 

89966 

88446 

11554 

10034 

21588 

32 

29 

78428 

89956 

88472 

11528 

10044 

21572 

*31 

30 

9.78445 

9.89947 

9.88498 

10.11502 

10.10053 

10.21555 

30 

31 

78461 

89937 

88524 

11476 

10063 

21539 

29 

32 

78478 

89927 

88550 

11450 

10073 

21522 

28 

33 

78494 

89918 

88577 

11423 

10082 

21506 

27 

34 

78510 

89908 

88603 

11397 

10092 

21490 

26 

35 

78527 

89898 

88629 

11371 

10102 

21473 

25 

36 

78543 

89888 

88655 

11345 

10112 

21457 

24 

37 

78560 

89879 

88681 

11319 

10121 

21440 

23 

38 

78576 

89869 

88707 

11293 

10131 

21424 

22 

39 

78592 

89859 

88733 

11267 

10141 

21408 

21 

40 

9.78609 

9.89849 

9.88759 

10.11241 

10.10151 

10.21391 

20 

41 

78625 

89840 

88786 

11214 

10160 

21375 

19 

42 

78642 

89830 

88812 

11188 

10170 

21358 

18 

43 

78658 

89820 

88838 

11162 

10180 

21342 

17 

44 

78674 

89810 

88864 

11136 

10190 

21326 

16 

45 

78691 

89801 

88890 

11110 

10199 

21309 

15 

46 

78707 

89791 

88916 

11084 

10209 

21293 

14 

47 

78723 

89781 

88942 

11058 

10219 

21277 

13 

48 

78739 

89771 

88968 

11032 

10229 

21261 

12 

49 

78756 

. 89761 

88994 

11006 

10239 

21244 

11 

50 

9.78772 

9.89752 

9.89020 

10.10980 

10.10248 

10.21228 

10 

51 

78788 

89742 

89046 

1&154 

10258 

21212 

9 

52 

78805 

89732 

89073 

10927 

10268 

21195 

8 

53 

78821 

89722 

89099 

10901 

10278 

21179 

7 

54 

78837 

89712 

89125 

10875 

10288 

21163 

6 

55 

78853 

89702 

89151 

10849 

10298 

21147 

5 

56 

78869 

89693 

89177 

10823 

10307 

21131 

4 

57 

78886 

89683 

89203 

10797 

10317 

21114 

3 

58 

78902 

89673 

89229 

10771 

10327 

21098 

2 

59 

78918 

89663 

89255 

10745 

10337 

21082 

1 

60 

78934 

89653 

89281 

10719 

10347 

21066 

0 

j Co-?inc. 

Sine. | 

Co-tang. 

Tangent. 

Co-secant 

Secant. 

M. 


T 52 Degrees 








































































146 Artificial Sines, Tang, and* Sec. 38 Degrees. 


M. 

Sine. 

Co-sine. 

Tangent. 

Co-tang. 

Secant. 

Co-secant 


0 

9.78934 

9.89653 

9.89281 

10.10719 

10.10347 

10.21066 

60 

1 

78950 

89643 

89307 

10693 

10357 

21050 

59 

2 

78967 

89633 

89333 

10667 

10367 

21033 

58 

3 

78983 

89624 

89359 

10641 

10376 

21017 

57 

4 

78999 

89614 

89385 

10615 

10386 

21001 

56 

5 

79015 

89604 

89411 

10589 

10396 

20985 

55 

G 

79031 

89594 

89437 

10563 

10406 

20969 

54 

7 

79047 

89584 

89463 

10537 

10416 

20953 

53 

8 

79063 

89574 

89489 

10511 

10426 

20937 

52 

9 

79079 

89564 

89515 

10485 

10436 

20921 

51 

10 

9.79095 

9.89554 

9.89541 

10.10459 

10.10446 

10.20905 

50 

11 

79111 

89544 

89567 

10433 

10456 

20889 

49 

12 

79128 

89534 

89593 

10407 

10466 

20872 

48 

13 

79144 

89524 

89619 

10381 

10476 

20856 

47 

14 

79160 

89514 

89645 

10355 

10486 

20840 

46 

15 

79176 

89504 

89671 

10329 

10496 

20824 

45 

16 

79192 

89495 

89697 

10303 

10505 

20808 

44 

17 

79208 

89485 

89723 

10277 

10515 

20792 

43 

18 

79224 

89475 

89749 

10251 

10525 

20776 

42 

19 

79240 

89465 

89775 

10225 

10535 

20760 

41 

20 

9.79256 

9.89455 

9.89801 

10.10199 

10.10545 

10.20744 

40 

21 

79272 

89445 

89827 

10173 

10555 

20728 

39 

22 

79288 

89435 

89853 

10147 

10565 

20712 

38 

23 

79304 

89425 

89879 

10121 

10575 

20696 

37 

24 

79319 

89415 

89905 

10095 

10585 

20681 

36 

25 

79335 

89405 

89931 

10069 

10595 

20665 

35 

26 

79351 

89395 

89957 

10043 

10605 

20649 

34 

27 

79367 

89385 

89983 

10017 

10615 

20633 

33 

28 

79383 

89375 

90009 

09991 

10625 

20617 

32 

29 

79399 

89364 

90035 

09965 

10636 

20601 

31 

30 

9.79415 

9.89354 

9.90061 

10.09939 

10.10646 

10.20585 

30 

31 

79431 

89344 

90086 

09914 

10656 

20569 

29 

32 

79447 

89334 

90112 

09888 

10666 

20553 

28 

33 

79463 

89324 

90138 

09862 

10676 

20537 

27 

34 

79478 

89314 

90164 

09836 

10686 

20522 

26 

35 

79494 

89304 

90190 

09810 

10696 

20506 

25 

36 

79510 

89294 

90216 

09784 

10706 

20490 

.24 

37 

79526 

89284 

90242 

09758 

10716 

20474 

23 

38 

79542 

89274 

90268 

09732 

10726 

20458 

22 

39 

79558 

89264 

90294 

09706 

10736 

20442 

21 

40 

9.79573 

9.89254 

9.90320 

10.09680 

10.10746 

10.20427 

20 

41 

79589 

89244 

90346 

09654 

10756 

20411 

19 

42 

79605 

89233 

90371 

09629 

10767 

20395 

18 

43 

79621 

89223 

90397 

09603 

10777 

20379 

17 

44 

79636 

89213 

90423 

09577 

10787 

20364 

16 

45 

79652 

89203 

90449 

09551 

10797 

20348 

15 

46 

79668 

89193 

90475 

09525 

10807 

20332 

14 

47 

79684 

89183 

90501 

09499 

10817 

20316 

13 

48 

79699 

89173 

90527 

09473 

10827 

20301 

12 

49 

79715 

89162 

90553 

09447 

10838 

20285 

11 

50 

9-79731 

9.89152 

9.90578 

10.09422 

10.10848 

10.20269 

10 

51 

79746 

89142 

90604 

09396 

10858 

20254 

9 

52 

79762 

89132 

90630 

09370 

10868 

20238 

8 

53 

79778 

89122 

90656 

09344 

10878 

20222 

7 

54 

79793 

89112 

90682 

09318 

10888 

20207 

6 

55 

79809 

89101 

90708 

09292 

10899 

20191 

5 

56 

79825 

89091 

90734 

09266 

10909 

20175 

4 

57 

79840 

89081 

90759 

09241 

10919 

20160 

3 

58 

79856 

89071 

90785 

09215 

10929 

20144 

2 

59 

79872 

89060 

90811 

09189 

10940 

20128 

1 

60 

79887 

89050 

90837 

09163 

10950 

20113 

0 


Co-sine. 

Sine. 

Co-tang. 

' Tangent. 

Co-secant 

Secant. 

M. 


51 Degrees* 













































































Artificial Sines, Tang, and Sec. 39 Degrees. 147 


M. 

Sine. 

Co-sine. 

Tangent. 

Co-tang. 

Secant. 

Co-secant 


0 

9.79887 

9.89050 

9.90837 

10.09163 

10.10950 

10.20113 

60 

1 

79903 

89040 

90863 

09137 

10960 

20097 

59 

2 

79918 

89030 

90889 

09111 

10970 

20082 

58 

3 

79934 

89020 

90914 

09086 

10980 

20066 

57 

4 

79950 

89009 

90940 

09060 

10991 

20050 

56 

5 

79965 

88999 

90966 

09034 

11001 

20035 

55 

6 

79981 

88989 

90992 

09008 

11011 

20019 

54 

7 

79996 

88978 

91018 

08982 

11022 

20004 

53 

8 

80012 

88968 

91043 

08957 

11032 

19988 

52 

9 

80027 

88958 

91069 

08931 

11042 

19973 

51 

10 

9.80043 

9.88948 

9.91095 

10.08905 

10.11052 

10.19957 

50 

11 

80058 

88937 

91121 

08879 

11063 

19942 

49 

12 

80074 

88927 

91147 

08853 

11073 

19926 

48 

13 

80089 

88917 

91172 

08828 

11083 

19911 

47 

14 

80105 

88906 

91198 

08802 

11094 

19895 

46 

15 

80120 

88896 

91224 

08776 

11104 

19880 

45 

16 

80136 

88886 

91250 

08750 

11114 

19864 

44 

17 

80151 

88875 

91276 

08724 

11125 

19849 

43 

18 

80166 

88865 

91301 

08699 

11135 

19834 

42 

19 

80182 

88855 

91327 

08673 

11145 

19818 

41 

| 20 

9.80197 

9.88844 

9.91353 

10.08647 

10.11156 

10.19803 

40 

: 21 

80213 

88834 

91379 

08621 

11166 

19787 

39 

! 22 

80228 

88824 

91404 

08596 

11176 

19772 

38 

1 23 

80244 

88813 

91430 

08570 

11187 

19756 

37 

24 

80259 

88803 

91456 

08544 

11197 

19741 

36 

25 

80274 

88793 

91482 

08518 

11207 

19726 

35 

26 

80290 

88782 

91507 

08493 

11218 

19710 

34 

27 

80305 

88772 

91533 

08467 

11228 

19695 

33 

28 

80320 

88761 

91559 

08441 

11239 

19680 

32 

29 

80336 

88751 

91585 

08415 

11249 

19664 

31 

30 

9.80351 

9.88741 

9.91610 

10.08390 

10.11259 

10.19649 

30 

31 

80366 

88730 

91636 

08364 

11270 

19634 

29 

32 

80382 

88720 

91662 

08338 

11280 

19618 

28 

33 

80397 

88709 

91688 

08312 

11291 

19603 

27 

34 

80412 

88699 

91713 

08287 

11301 

19588 

26 

35 

80428 

88688 

91739 

08261 

11312 

19572 

25 

36 

80443 

88678 

91765 

08235 

11322 

19557 

24 

37 

80458 

88668 

91791 

08209 

11332 

19542 

23 

38 

80473 

88657 

91816 

08184 

11343 

19527 

22 

39 

80489 

88647 

91842 

08158 

11353 

19511 

21 

40 

9.80504 

9.88636 

9.91868 

10.08132 

10.11364 

10.19496 

20 

41 

80519 

88626 

91893 

08107 

11374 

19481 

19 

42 

80534 

88615 

91919 

08081 

11385 

19466 

18 

43 

80550 

88605 

91945 

08055 

11395 

19450 

17 

44 

80565 

88594 

91971 

08029 

11406 

19435 

16 

45 

80580 

88584 

91996 

08004 

11416 

19420 

15 

46 

80595 

88573 

92022 

07978 

11427 

19405 

14 

47 

80610 

88563 

92048 

07952 

11437 

19390 

13 

48 

80625 

88552 

92073 

07927 

11448 

19375 

12 

i 

49 

80641 

88542 

92099 

07901 

11458 

19359 

11 

50 

9.80656 

9.88531 

9.92125 

10.07875 

10.11469 

10.19344 

10 

51 

80671 

88521 

92150 

07850 

11479 

19329 

9 

52 

80686 

88510 

92176 

07824 

11490 

19314 

8 

53 

80701 

88499 

92202 

07798 

11501 

19299 

7 

54 

80716 

88489 

92227 

07773 

11511 

19284 

6 

55 

80731 

88478 

92253 

07747 

11522 

19269 

5 

56 

80746 

88468 

92279 

07721 

11532 

19254 

4 

57 

80762 

88457 

92304 

07696 

11543 

19238 

3 

58 

80777 

88447 

92330 

07670 

11553 

19223 

2 ! 

59 

80792 

88436 

92356 

07644 

11564 

19208 

1 I 

60 

80807 

88425 

92381 

07619 

11575 

19193 

0 

• 

Co-sine. 

Sine. 

Co-tang. 

Tangent. 

Co-secant 

Secant. 

M. 


50 Degrees. 






































































































148 Artificial Sines, Tang, and Sec. 40 Degrees 


M. 

Sine. 

Co-sine. 

Tangent. | 

Co-tang. 

Secant. 1 

Co-secant 


0 

9.80807 

9.88425 

9.92381 

10.07619 

10.11575 

10.19193 

60 

1 

80822 

88415 

92407 

07593 

11585 

19178 

59 

2 

80837 

88404 

92433 

07567 

11596 

19163 

58 

3 

80852 

88394 

92458 

07542 

11606 

19148 

57 

4 

80867 

88383 

,92484 

07516 

11617 

19133 

56 

5 

80882 

88372 

92510 

07490 

11628 

19118 

55 

6 

80897 

88362 

92535 

07465 

11638 

19103 

54 

7 

80912 

88351 

92561 

07439 

11649 

19088 

53 

8 

80927 

88340 

92587 

07413 

11660 

19073 

52 

9 

80942 

88330 

92612 

07388 

11670 

19058 

51 

10 

9.80957 

9.88319 

9.92638 

10.07362 

10.11681 

10.19043 

50 

11 

80972 

88308 

92663 

07337 

11692 

19028 

49 

12 

80987 

88298 

92689 

07311 

11702 

19013 

48 

13 

81002 

88287 

92715 

07285 

11713 

18998 

47 j 

14 

81017 

88276 

92740 

07260 

11724 

18983 

46 | 

15 

81032 

88266 

92766 

07234 

11734 

18968 

45 

16 

81047 

88255 

92792 

07208 

11745 

18953 

44 

17 

81061 

88244 

92817 

07183 

11756 

18939 

43 

18 

81076 

88234 

92843 

07157 

11766 

18924 

42 

19 

81091 

88223 

92868 

07132 

11777 

18909 

41 

20 

9.81106 

9.88212 

9.92894 

10.07106 

10.11788 

10.18894 

40 

21 

81121 

88201 

92920 

07080 

11799 

18879 

39 

22 

81136 

88191 

92945 

07055 

11809 

18864 

38 

23 

81151 

88180 

92971 

07029 

11820 

18849 

37 

24 

81166 

88169 

92996 

07004 

11831 

18834 

36 

25 

81180 

88158 

93022 

06978 

11842 

18820 

35 

26 

81195 

88148 

93048 

06952 

11852 

18805 

34 

27 

81210 

88137 

93073 

06927 

11863 

18790 

33 

28 

81225 

88126 

93099 

06901 

11874 

18775 

32 

29 

81240 

88115 

93124 

06876 

11885 

18760 

31 

30 

9.81254 

9.88105 

9.93150 

10.06850 

10.11895 

10.18746 

30 

31 

81269 

88094 

93175 

06825 

11906 

18731 

29 

32 

81284 

88083 

93201 

06799 

11917 

18716 

28 

33 

81299 

88072 

93227 

06773 

11928 

18701 

27 

34 

81314 

88061 

93252 

06748 

11939 

18686 

26 

35 

81328 

88051 

93278 

06722 

11949 

18672 

25 

36 

81343 

88040 

93303 

06697 

11960 

18657 

24 

37 

81358 

88029 

93329 

06671 

11971 

18642 

23 

38 

81372 

88018 

93354 

06646 

11982 

18628 

22 

39 

81387 

88007 

93380 

06620 

11993 

18613 

21 

40 

9.81402 

9.87996 

9.93406 

10.06594 

10.12004 

10.18598 

20 

41 

81417 

87985 

93431 

06569 

12015 

18583 

19 

42 

81431 

87975 

93457 

06543 

12025 

18569 

18 

43 

81446 

87964 

93482 

06518 

12036 

18554 

17 

44 

81461 

87953 

93508 

06492 

12047 

18539 

16 

45 

81475 

87942 

93533 

06467 

12058 

18525 

15 

46 

81490 

87931 

93559 

06441 

12069 

18510 

14 

47 

81505 

87920 

93584 

06416 

12080 

18495 

13 

48 

81519 

87909 

93610 

06390 

12091 

18481 

12 

49 

81534 

87898 

93636 

06364 

12102 

18466 

11 

50 

9.81549 

9.87887 

9.93661 

10.06339 

10.12113 

10.18451 

10 

51 

81563 

87877 

93687 

06313 

12123 

18437 

9 

52 

81578 

87866 

93712 

06288 

12134 

18422 

8 

53 

81592 

87855 

93738 

06262 

12145 

18408 

7 

54 

81607 

87844 

93763 

06237 

12156 

18393 

6 

' 55 

81622 

87833 

93789 

06211 

12167 

18378 

5 

56 

81636 

87822 

93814 

06186 

12178 

18364 

4 

57 

81651 

87811 

93840 

06160 

12189 

18349 

3 

58 

81665 

87800 

93865 

06135 

12200 

18335 

2 

59 

81680 

87789 

93891 

06109 

12211 

18320 

1 

60 

81694 

87778 

93916 

06084 

12222 

18306 

0 

—.— 

Co-sine. 

Sine. 

Co-tang. 

I Tangent. 

Co-secant 

Secant. 

M. 


49 Degrees. 

























































































Artificial Sines, Tang, and Sec. 41 Degrees. 149 


|M._ 

Sine. 

Co-sine. 

Tangent. 

Co-tang. 

Secant. 

Co-secant 


0 

9.81694 

9.87778 

9.93916 

10.06084 

10.12222 

10.18306 

60 

1 

81709 

87767 

93942 

06058 

12233 

18291 

59 

2 

81723 

87756 

93967 

06033 

12244 

18277 

58 

3 

81738 

87745 

93993 

06007 

12255 

18262 

57 

4 

81752 

87734 

94018 

05982 

12266 

18248 

56 

5 

81767 

87723 

94044 

05956 

12277 

18233 

55 

6 

81781 

87712 

94069 

05931 

12288 

18219 

54 

7 

81796 

87701 

94095 

05905 

12299 

18204 

53 

8 

81810 

87690 

94120 

05880 

12310 

18190 

52 

9 

81825 

87679 

94146 

05854 

12321 

18175 

51 

10 

9.81839 

9.87668 

9.94171 

10.05829 

10.12332 

10.18161 

50 

11 

81854 

87657 

94197 

05803 

12343 

18146 

49 

12 

81868 

87646 

94222 

05778 

12354 

18132 

48 

13 

81882 

87635 

94248 

05752 

12365 

18118 

47 

14 

81897 

87624 

94273 

05727 

12376 

18103 

46 

15 

81911 

87613 

94299 

05701 

12387 

18089 

45 

16 

81926 

87601 

94324 

05676 

12399 

18074 

44 

17 

81940 

87590 

94350 

05650 

12410 

18060 

43 

18 

81955 

87579 

94375 

05625 

12421 

18045 

42 

19 

81969 

87568 

94401 

05599 

12432 

18031 

41 

20 

9.81983 

9.87557 

9.94426 

10.05574 

10.12443 

10.18017 

40 

21 

81998 

87546 

94452 

05548 

12454 

18002 

39 

22 

82012 

87535 

94477 

05523 

12465 

17988 

38 

23 

82026 

87524 

94503 

05497 

12476 

17974 

37 

24 

82041 

87513 

94528 

05472 

12487 

17959 

36 

25 

82055 

C7501 

94554 

05446 

12499 

17945 

35 

26 

82069 

87490 

94579 

05421 

12510 

17931 

34 

27 

82084 

87479 

94604 

05396 

12521 

17916 

33 

28 

82098 

87468 

94630 

05370 

12532 

17902 

32 

29 

82112 

87457 

94655 

05345 

12543 

17888 

31 

30 

9.82126 

9.87446 

9.94681 

10.05319 

10.12554 

10.17874 

30 

31 

82141 

87434 

94706 

05294 

12566 

f7859 

29 

32 

82155 

87423 

94732 

05268 

12577 

17845 

28 

33 

82169 

87412 

94757 

05243 

12588 

17831 

27 

34 

82184 

87401 

94783 

05217 

12599 

17816 

26 

35 

82198 

87390 

94808 

05192 

12610 

17802 

25 

36 

82212 

87378 

94834 

05166 

12622 

17788 

24 

37 

82226 

87367 

94859 

05141 

12633 

17774 

23 

38 

82240 

87356 

94884 

05116 

12644 

17760 

00 

39 

82255 

87345 

94910 

05090 

12655 

17745 

21 

40 

9.82269 

9.87334 

9.94935 

10.05065 

10.12666 

10.17731 

20 

41 

82283 

87322 

94961 

05039 

12678 

17717 

19 

42 

82297 

87311 

94986 

05014 

12689 

17703 

18 

43 

82311 

87300 

95012 

04988 

12700 

17689 

17 

44 

82326 

87288 

95037 

04963 

12712 

17674 

16 

45 

82340 

87277 

95062 

04938 

12723 

17660 

15 

46 

82354 

87266 

95088 

04912 

12734 

17646 

14 

47 

82368 

87255 

95113 

04887 

12745 

17632 

13 

48 

82382 

87243 

95139 

04861 

12757 

17618 

12 

49 

82396 

87232 

95164 

04836 

12768 

17604 

11 

50 

9.82410 

9.87221 

9.95190 

10.04810 

10.12779 

10.17590 

10 

51 

82424 

87209 

95215 

04785 

12791 

17576 

9 

52 

82439 

87198 

95240 

04760 

12802 

17561 

8 

53 

82453 

87187 

95266 

04734 

12813 

17547 

7 

54 

82467 

87175 

95291 

04709 

12825 

17533 

6 

55 

82481 

87164 

95317 

04683 

12836 

17519 

5 

56 

82495 

87153 

95342 

04658 

12847 

17505 

4 

57 

82509 

87141 

95368 

04632 

12859 

17491 

3 

58 

82523 

87130 

95393 

04607 

12870 

17477 

2 

59 

82537 

87119 

95418 

04582 

12881 

17463 

1 

60 

82551 

87107 

95444 

04556 

12893 

17449 

0 

1 Co-sine. 

Sine. 

Co-tang. 

Tangent. 

Co-secant 

Secant. 

M. 


48 Degrees. 




















































































1.00 Artificial Sines, Tang, and Sec. 42 Degrees. 


M. 

Sine. 

Co-sine. 

Tangent. 

Co-tang. 

Secant. 

Co-secant 


0 

9.82551 

9.87107 

9.95444 

10.04556 

10.12893 

10.17449 

60 

1 

82565 

87096 

95469 

04531 

12904 

17435 

59 

2 

82579 

87085 

95495 

04505 

12915 

17421 

58 

3 

82593 

87073 

95520 

04480 

12927 

17407 

57 

4 

82607 

87062 

95545 

04455 

12938 

i:393 

56 

5 

82621 

87050 

95571 

04429 

12950 

17379 

55 

0 

82635 

87039 

95596 

04404 

12961 

17365 

54 

7 

82649 

87028 

95622 

04378 

12972 

17351 

53 

8 

82663 

87016 

95647 

04353 

12984 

17337 

52 

9 

82677 

87005 

95672 

04328 

12995 

17323 

51 

10 

9.82691 

9.86993 

9.95698 

10.04302 

10.13007 

10.17309 

50 

11 

82705 

86982 

95723 

04277 

13018 

17295 

49 

12 

82719 

86970 

95748 

04252 

13030 

17281 

48 

13 

82733 

86959 

95774 

04226 

13041 

17267 

47 

14 

82747 

86947 

95799 

04201 

13053 

17253 

46 

15 

82761 

86936 

95825 

04175 

13064 

17239 

45 

16 

82775 

86924 

95850 

04150 

13076 

17225 

44 

17 

82788 

86913 

95875 

04125 

13087 

17212 

43 

18 

82802 

86902 

95901 

04099 

13098 

17198 

42 

19 

82816 

86890 

95926 

04074 

13110 

17184 

41 

20 

9.82830 

9.86879 

9.95952 

10.04048 

10.13121 

10.17170 

40 

21 

82844 

86867 

95977 

04023 

13133 

17156 

39 

22 

82858 

86855 

96002 

03998 

13145 

17142 

38 

23 

82872 

86844 

96028 

03972 

13156 

17128 

37 

24 

82885 

86832 

96053 

03947 

13168 

17115 

36 

25 

82899 

86821 

* 96078 

03922 

13179 

17101 

35 

26 

82913 

86809 

96104 

03896 

13191 

17087 

34 

27 

82927 

86798 

96129 

03871 

13202 

17073 

33 

28 

82941 

86786 

96155 

03845 

13214 

17059 

32 

29 

82955 

86775 

96180 

03820 

13225 

17045 

31 

30 

9.82968 

9.86763 

9.96205 

10.03795 

10.13237 

10.17032 

30 

31 

82982 

86752 

96231 

03769 

13248 

17018 

29 

32 

82996 

86740 

96256 

03744 

13260 

17004 

28 

33 

83010 

86728 

96281 

03719 

13272 

16990 

27 

34 

83023 

86717 

96307 

03693 

13283 

16977 

26 

35 

83037 

86705 

96332 

03668 

13295 

16963 

25 

36 

83051 

86694 

96357 

03643 

13306 

16949 

24 

37 

83065 

86682 

96383 

03617 

13318 

16935 

23 

38 

83078 

86670 

96408 

03592 

13330 

16922 

22 

39 

83092 

86659 

96433 

03567 

13341 

16908 

21 

40 

: .83106 

9.86647 

9.96459 

10.03541 

10.13353 

10.16894 

20 

41 

83120 

86635 

96484 

03516 

13365 

16880 

19 

42 

83133 

86624 

96510 

03490 

13376 

16867 

18 

43 

83147 

86612 

96535 

03465 

13388 

16853 

17 

44 

83161 

86600 

96560 

03440 

13400 

16839 

16 

45 

83174 

86589 

96586 

03414 

13411 

16826 

15 

46 

83188 

86577 

96611 

03389 

13423 

16812 

14 

47 

83202 

86565 

96636 

03364 

13435 

16798 

13 

48 

83215 

86554 

96662 

03338 

13446 

16785 

12 

49 

83229 

86542 

96687 

03313 

13458 

16771 

11 

50 

J .83242 

9.86530 

9:96712 

10.03288 

10.13470 

10.16758 

10 

51 

83256 

86518 

96738 

03262 

13482 

16744 

9 

52 

83270 

86507 

96763 

03237 

13493 

16730 

8 ! 

53 

83283 

86495 

96788 

03212 

13505 

16717 

7 1 

54 

83297 

86483 

96814 

03186 

13517 

16703 

6 i 

55 

83310 

86472 

96839 

03161 

13528 

16690 

5 

56 

83324 

86460 

96864 

03136 

13540 

16676 

4 1 

57 

83338 

86448 

96890 

03110 

13552 

16662 

31 

58 

83351 

86436 

96915 

03085 

13564 

16649 

2-4 

59 

83365 

86425 

96940 

03060 

13575 

*16635 

1 j 

60 

83378 

86413 

96966 

03034 

13587 

16622 

0 1 

1 Co-sine. 


Co-tang. 

Tangent. 

Co-secant 

Secant. 

M. j 


*** ~^^**-' r,> Tf--nTrr‘Trr , irfjaiiirtnf‘iii>>ia>giiMMwiiiijni'<—Mimw nn—winy m.u 


47 Degrees 






















































































Artificial Sines, Tang, and Sec. 43 Degrees. 151 


1YJL 

Sine. 

Co-sine. 

Tangent. 

Co-tang. 

Secant. 1 

Co-secant j 


0 

9.83378 

9.86413 

9.96966 

10.03034 

10.13587 

10.16622 

60 

1 

83392 

86401 

96991 

03009 

13599 

16608 

59 

2 

83405 

86389 

97016 

02984 

13611 

16595 

58 

3 

83419 

86377 

97042 

02958 

13623 

16581 

57 t 

4 

83432 

86366 

97067 

02933 

13634 

16568 

56 1 

5 

83446 

86354 

97092 

02908 

13646 

16554 

55 

6 

83459 

86342 

97118 

02882 

13658 

16541 

54 1 

7 

83473 

86330 

97143 

02857 

13670 

16527 

53 

8 

83486 

86318 

97168 

02832 

13682 

16514 

52 

9 

83500 

86306 

97193 

02807 

13694 

16500 

51 | 

10 

9.83513 

9.86295 

9.97219 

10.02781 

10.13705 

10.16487 

50 

H 

83527 

86283 

97244 

02756 

13717 

16473 

49 

12 

83540 

86271 

97269 

02731 

13729 

16460 

48 

13 

83554 

86259 

97295 

02705 

13741 

16446 

47 

14 

83567 

86247 

97320 

02680 

13753 

16433 

46 

15 

83581 

86235 

97345 

02655 

13765 

16419 

45 

16 

83594 

86223 

97371 

02629 

13777 

16406 

44 

17 

83608 

86211 

97396 

02604 

13789 

16392 

43 

13 

83621 

86200 

97421 

02579 

13800 

16379 

42 1 

19 

83634 

86188 

97447 

02553 

13812 

16366 

41 

20 

9.83648 

9.86176 

9.97472 

10.02528 

10.13824 

10.16352 

40 

21 

83661 

86164 

97497 

02503 

13836 

16339 

39 

22 

83674 

86152 

97523 

02477 

13848 

16326 

38 

23 

83688 

86140 

97548 

02452 

13860 

16312 

37 

24 

83701 

86128 

97573 

02427 

13872 

16299 

36 

25 

83715 

86116 

97598 

02402 

13884 

16285 

35 

26 

83728 

86104 

97624 

02376 

13896 

16272 

34 

27 

83741 

86092 

97649 

02351 

13908 

16259 

33 

28 

83755 

86080 

97674 

02326 

13920 

16245 

32 

29 

83768 

86068 

97700 

02300 

13932 

16232 

31 

30 

9.83781 

9.86056 

9.97725 

10.02275 

10.13944 

10.16219 

30 

31 

83795 J 

86044 

97750 

02250 

13956 

16205 

29 

32 

83808 

86032 

97776 

02224 

13968 

16192 

28 

33 

83821 

86020 

97801 

02199 

13980 

16179 

27 

34 

83834 

86008 

97826 

02174 

13992 

16166 

26 

35 

v 83848 

85996 

97851 

02149 

14004 

16152 

25 

36 

83861 

85984 

97877 

02123 

14016 

16139 

24 

37 

83874 

85972 

97902 

02098 

14028 

16126 

23 

38 

83887 

85960 

97927 

02073 

14040 

16113 

22 

39 

83901 

85948 

97953 

02047 

14052 

16099 

21 

40 

9.83914 

9.85936 

9.97978 

10.02022 

10.14064 

10.16086 

20 

41 

83927 

85924 

98003 

01997 

14076 

16073 

19 

42 

83940 

85912 

98029 

01971 

14088 

16060 

18 

43 

83954 

85900 

98054 

01946 

14100 

16046 

17 

44 

83967 

85888 

98079 

01921 

14112 

16033 

16 

45 

83980 

85876 

98104 

01896 

14124 

16020 

15 

46 

83993 

85864 

98130 

01870 

14136 

16007 

14 

47 

84006 

85851 

98155 

01845 

14149 

15994 

13 

48 

84020 

85839 

98180 

01820 

14161 

15980 

12 

49 

84033 

85827 

98206 

01794 

14173 

15967 

11 

50 

9.84046 

9.85815 

9.98231 

10.01769 

10.14185 

10.15954 

10 

51 

84059 

85803 

98256 

01744 

14197 

15941 

9 

52 

84072 

85791 

98281 

01719 

14209 

15928 

8 

53 

84085 

85779 

98307 

01693 

14221 

15915 

7 

54 

84098 

85766 

98332 

01668 

14234 

15902 

6 

55 

84112 

85754 

98357 

0J 643 

14246 

15888 

5 

56 

84125 

85742 

98383 

01617 

14258 

15875 

4 

57 

84138 

85730 

98408 

01592 

14270 

15862 

3 

1 58 

84151 

85718 

98433 

01567 

14282 

15849 

2 

59 

84164 

85706 

98458 

01542 

14294 

15836 

J 

60 

84177 

85693 

98484 

01516 

14307 

15823 

0 


Co-sine. 

Sine. 

Co-tang. 

Tangent. 

Co-secant 

Secant. 

M. 




- 46 Degrees. 































































































152 


Artificial Sines, Tang, and Sec. 44 Degrees 


M. 

Sine. 

Co-sine. 

Tangent. 

1 Co-tang. 

Secant. 

j Co-secant 


! o 

9.84177 

9.85693 

9.98484 

10.01516 

10.14307 

10.15823 

60 

l 

84190 

85681 

98509 

01491 

14319 

15810 

59 

[ 2 

84203 

85669 

98534 

01466 

14331 

15797 

58 

1 3 

84216 

85657 

98560 

01440 

14343 

15784 

57 

4 

84229 

85645 

98585 

01415 

14355 

15771 

56 

5 

84242 

85632 

98610 

01390 

14368 

15758 

55 

6 

84255 

85620 

98635 

01365 

14380 

15745 

54 

7 

84269 

85608 

98661 

01339 

14392 

15731 

53 

8 

84282 

8559ft 

98686 

01314 

14404 

15718 

52 

9 

84295 

85583 

98711 

01289 

14417 

15705 

51 

10 

9.84308 

9.85571 

9.98737 

10.01263 

10.14429 

10.15692 

50 

11 

84321 

85559 

98762 

01238 

14441 

15679 

49 

12 

84334 

85547 

98787 

01213 

14453 

15666 

48 

13 

84347 

85534 

98812 

01188 

14466 

15653 

47 

14 

84360 

85522 

98838 

01162 

14478 

15640 

46 

15 

84373 

85510 

98863 

01137 

14490 

15627 

45 

16 

84385 

85497 

98888 

01112 

14503 

15615 

44 

17 

84398 

85485 

98913 

01087 

14515 

15602 

43 

18 

84411 

85473 

98939 

01061 

14527 

15589 

42 

19 

84424 

85460 

98964 

01036 

14540 

15576 

41 

20 

9.84437 

9.85448 

9.98989 

10.01011 

10.14552 

10.15563 

40 

21 

84450 

85436 

99015 

00985 

14564 

15550 

39 

22 

84463 

85423 

99040 

00960 

14577 

15537 

38 

23 

84476 

85411 

99065 

00935 

14589 

15524 

37 

24 

84489 

85399 

99090 

00910 

14601 

15511 

36 

25 

84502 

85386 

99116 

00884 

14614 

15498 

35 

26 

84515 

85374 

99141 

00859 

14626 

15485 

34 

27 

84528 

85361 

99166 

00834 

14639 

15472 

33 

28 

84540 

85349 

99191 

00809 

14651 

15460 

32 

29 

84553 

85337 

99217 

00783 

14663 

15447 

31 

30 

9.84566 

9.85324 

9.99242 

10.00758 

10.14676 

10.15434 

30 

31 

84579 

85312 

99267 

00733 

14688 

15421 

29 

32 

84592 

85299 

99293 

00707 

14701 

15408 

28 

33 

84605 

85287 

99318 

00682 

14713 

15395 

27 

34 

84618 

85274 

99343 

00657 

14726 

15382 

26 

35 

84630 

85262 

99368 

00632 

14738 

15370 

25 

36 

84643 

85250 

99394 

00506 

14750 

15357 

24 

37 

84656 

85237 

99419 

00581 

14763 

15344 

23 

38 

84669 

85225 

99444 

00556 

14775 

15331 

22 

39 

84682 

85212 

99469 

00531 

14788 

15318 

21 

40 

9.84694 

9.85200 

9.99495 

10.00505 

10.14800 

10.15306 

20 

41 

84707 

85187 

99520 

00480 

14813 

15293 

19 

42 

84720 

85175 

99545 

00455 

14825 

15280 

18 

43 

84733 

85162 

99570 

00430 

14838 

15267 

17 

44 

84745 

85150 

99596 

00404 

14850 

15255 

16 

45 

84758 

85137 

99621 

00379 

14863 

15242 

15 

46 

84771 

85125 

99646 

00354 

14875 

15229 

14 

47 

84784 

85112 

99672 

00328 

14888 

15216 

13 

48 

84796 

85100 

99697 

00303 

14900 

15204 

12 

49 

84809 

85087 

99722 

00278 

14913 

15191 

11 

50 

9.84822 

9.85074 

9.99747 

10.00253 

10.14926 

10.15178 

10 

51 

84835 

85062 

99773 

00227 

14938 

15165 

9 

52 

84847 

85049 

99798 

00202 

14951 

15153 

8 

53 

84860 

85037 

99823 

00177 

14963 

15140 

7 

54 

84873 

85024 

99848 

00152 

14976 

15127 

6 

55 

84885 

85012 

99874 

00126 

14988 

15115 

5 

56 

84898 

84999 

99899 

00101 

15001 

15102 

4 

57 

84911 

84986 

99924 

00076 

15014 

15089 

3 

58 

84923 

84974 

99949 

00051 

15026 

15077 

2 

59 

84936 

84961 

99975 

00025 

15039 

15064 

1 

60 

84949 

84949 

10.00000 

10.00000 

15051 

15051 

0 


Co-sine. 

Sine. 

Co-tang. 

Tangent. 

Co-secant 

Secant. 

M. 


45 Degrees 



























































































































































1’late 



























































































































































































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Plate 4. 



<pg§l 

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mm 




1 

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t j i 

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. T.S ~T~ 

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i’late 6. 
































































































































/ 



LHate 8. 


100 


LOT 


106 


I08 


loo 


































































V: J 

: 

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1 : . 

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> a , 

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H5R. ARY 0F CONGRESS 


0 019 408 685 f, 









